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1.

図書
図書
1. Selected papers of E.B. Dynkin with commentary
E.B. Dynkin ; A.A. Yushkevich, G.M. Seitz, A.L. Onishchik, editors
出版情報: Providence, R.I. : American Mathematical Society , Cambridge, Mass. : International Press, c2000  xxvi, 798 p. ; 27 cm
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Lie groups and Lie algebras: Dynkin and Lie theory / G. M. SeitzPart I：
On the work of E. B. Dynkin in the theory of Lie groups / F. I. Karpelevich ; A. L. Onishchik ; E. B. Vinberg
Correction to On the work of E. B. Dynkin in the theory of Lie groups
Classification of simple Lie groups / E. B. Dynkin
Calculation of the coefficients in the Campbell-Hausdorff formula
The maximal subgroups of the classical groups
Comments on Maximal subgroups of the classical groups
Semisimple subalgebras of semisimple Lie algebras
Comments on the paper Semisimple subalgebras of semisimple Lie algebras
Construction of primitive cycles in compact Lie groups
Topological characteristics of homomorphisms of compact Lie groups
Comments on the paper Topological characteristics of homomorphisms of compact Lie groups
Dynkin and modern Lie theory / B. Kostant
Comments on the impact of Dynkin's work on current research in representation theory / D. A. Vogan
Coxeter-Dynkin diagrams and singularities / A. Gabrielov
Lie groups in physics / K. Gottfried
Dynkin diagrams in the physics of particles, fields and strings / Y. Ne'eman
Probability theory: Dynkin and probability theory / A. A. YushkevichPart II：
Necessary and sufficient statistics for a family of probability distributions
Some limit theorems for sums of independent random variables with infinite mathematical expectations
Markov processes and semigroups of operators
Strong Markov processes
Infinitesimal operators of Markov processes
The natural topology and excessive functions connected with a Markov process
Random walk on groups with a finite number of generators / M. B. Malyutov
The optimum choice of the instant for stopping a Markov process
Brownian motion in certain symmetric spaces and nonnegative eigenfunctions of the Laplace-Beltrami operator
Diffusion of tensors
Game variant of a problem on optimal stopping
Determining functions of Markov processes and corresponding dual regular classes / S. E. Kuznetsov
Economic equilibrium under uncertainty
Comments on Economic equilibrium under uncertainty / I. V. Evstigneev
Markov processes and random fields
Green's and Dirichlet spaces associated with fine Markov processes
Markov processes as a tool in field theory
Symmetric statistics, Poisson point processes, and multiple Wiener integrals / A. Mandelbaum
Gaussian and non-Gaussian random fields associated with Markov processes
Author's correction to Guassian and non-Gaussian random fields associated with Markov processes.
An application of flows to time shift and time reversal in stochastic processes
Author's comments on An application of flows to time shift and time reversal in stochastic processes
Representation for functionals of superprocesses by multiple stochastic integrals, with applications to self-intersection local times
A probabilistic approach to one class of nonlinear differential equations
Superdiffusions and parabolic nonlinear differential equations
Comments on Superdiffusions and parabolic nonlinear differential equations
Dynkin and the theory of Markov processes / P. A. Meyer
To the history of strong Markov property
On compactifications of symmetric spaces / M. A. Olshanetsky
Dynkin's contributions to superprocesses and partial differential equations / J.-F. Le Gall
Dynkin's work in mathematical economics
Acknowledgments
Lie groups and Lie algebras: Dynkin and Lie theory / G. M. SeitzPart I：
On the work of E. B. Dynkin in the theory of Lie groups / F. I. Karpelevich ; A. L. Onishchik ; E. B. Vinberg
Correction to On the work of E. B. Dynkin in the theory of Lie groups
2.

図書
図書
2. Probability, reliability and statistical methods in engineering design
Achintya Haldar, Sankaran Mahadevan
出版情報: New York ; Chichester : Wiley, c2000  xvi, 304 p. ; 25 cm
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Basic Concept of Reliability
Mathematics of Probability
Modeling of Uncertainty
Commonly Used Probability Distributions
Determination of Distributions and Parameters from Observed Data
Randomness in Response Variables
Fundamentals of Reliability Analysis
Advanced Topics on Reliability Analysis
Simulation Techniques
Appendices
Conversion Factors
References
Index
Basic Concept of Reliability
Mathematics of Probability
Modeling of Uncertainty
3.

図書
図書
3. Statistical inference. 2nd ed
George Casella, Roger L. Berger
出版情報: Belmont, Calif. : Brooks/Cole, c2002  xxviii, 660 p. ; 25 cm
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Probability Theory / 1：
Set Theory / 1.1：
Basics of Probability Theory / 1.2：
Axiomatic Foundations / 1.2.1：
The Calculus of Probabilities / 1.2.2：
Counting / 1.2.3：
Enumerating Outcomes / 1.2.4：
Conditional Probability and Independence / 1.3：
Random Variables / 1.4：
Distribution Functions / 1.5：
Density and Mass Functions / 1.6：
Exercises / 1.7：
Miscellanea / 1.8：
Transformations and Expectations / 2：
Distributions of Functions of a Random Variable / 2.1：
Expected Values / 2.2：
Moments and Moment Generating Functions / 2.3：
Differentiating Under an Integral Sign / 2.4：
Common Families of Distributions / 2.5：
Introduction / 3.1：
Discrete Distributions / 3.2：
Continuous Distributions / 3.3：
Exponential Families / 3.4：
Location and Scale Families / 3.5：
Inequalities and Identities / 3.6：
Probability Inequalities / 3.6.1：
Identities / 3.6.2：
Multiple Random Variables / 3.7：
Joint and Marginal Distributions / 4.1：
Conditional Distributions and Independence / 4.2：
Bivariate Transformations / 4.3：
Hierarchical Models and Mixture Distributions / 4.4：
Covariance and Correlation / 4.5：
Multivariate Distributions / 4.6：
Inequalities / 4.7：
Numerical Inequalities / 4.7.1：
Functional Inequalities / 4.7.2：
Properties of a Random Sample / 4.8：
Basic Concepts of Random Samples / 5.1：
Sums of Random Variables from a Random Sample / 5.2：
Sampling from the Normal Distribution / 5.3：
Properties of the Sample Mean and Variance / 5.3.1：
The Derived Distributions: Student's t and Snedecor's F / 5.3.2：
Order Statistics / 5.4：
Convergence Concepts / 5.5：
Convergence in Probability / 5.5.1：
Almost Sure Convergence / 5.5.2：
Convergence in Distribution / 5.5.3：
The Delta Method / 5.5.4：
Generating a Random Sample / 5.6：
Direct Methods / 5.6.1：
Indirect Methods / 5.6.2：
The Accept/Reject Algorithm / 5.6.3：
Principles of Data Reduction / 5.7：
The Sufficiency Principle / 6.1：
Sufficient Statistics / 6.2.1：
Minimal Sufficient Statistics / 6.2.2：
Ancillary Statistics / 6.2.3：
Sufficient, Ancillary, and Complete Statistics / 6.2.4：
The Likelihood Principle / 6.3：
The Likelihood Function / 6.3.1：
The Formal Likelihood Principle / 6.3.2：
The Equivariance Principle / 6.4：
Point Estimation / 6.5：
Methods of Finding Estimators / 7.1：
Method of Moments / 7.2.1：
Maximum Likelihood Estimators / 7.2.2：
Bayes Estimators / 7.2.3：
The EM Algorithm / 7.2.4：
Methods of Evaluating Estimators / 7.3：
Mean Squared Error / 7.3.1：
Best Unbiased Estimators / 7.3.2：
Sufficiency and Unbiasedness / 7.3.3：
Loss Function Optimality / 7.3.4：
Hypothesis Testing / 7.4：
Methods of Finding Tests / 8.1：
Likelihood Ratio Tests / 8.2.1：
Bayesian Tests / 8.2.2：
Union-Intersection and Intersection-Union Tests / 8.2.3：
Methods of Evaluating Tests / 8.3：
Error Probabilities and the Power Function / 8.3.1：
Most Powerful Tests / 8.3.2：
Sizes of Union-Intersection and Intersection-Union Tests / 8.3.3：
p-Values / 8.3.4：
Interval Estimation / 8.3.5：
Methods of Finding Interval Estimators / 9.1：
Inverting a Test Statistic / 9.2.1：
Pivotal Quantities / 9.2.2：
Pivoting the CDF / 9.2.3：
Bayesian Intervals / 9.2.4：
Methods of Evaluating Interval Estimators / 9.3：
Size and Coverage Probability / 9.3.1：
Test-Related Optimality / 9.3.2：
Bayesian Optimality / 9.3.3：
Asymptotic Evaluations / 9.3.4：
Consistency / 10.1：
Efficiency / 10.1.2：
Calculations and Comparisons / 10.1.3：
Bootstrap Standard Errors / 10.1.4：
Robustness / 10.2：
The Mean and the Median / 10.2.1：
M-Estimators / 10.2.2：
Asymptotic Distribution of LRTs / 10.3：
Other Large-Sample Tests / 10.3.2：
Approximate Maximum Likelihood Intervals / 10.4：
Other Large-Sample Intervals / 10.4.2：
Analysis of Variance and Regression / 10.5：
Oneway Analysis of Variance / 11.1：
Model and Distribution Assumptions / 11.2.1：
The Classic ANOVA Hypothesis / 11.2.2：
Inferences Regarding Linear Combinations of Means / 11.2.3：
The ANOVA F Test / 11.2.4：
Simultaneous Estimation of Contrasts / 11.2.5：
Partitioning Sums of Squares / 11.2.6：
Simple Linear Regression / 11.3：
Least Squares: A Mathematical Solution / 11.3.1：
Best Linear Unbiased Estimators: A Statistical Solution / 11.3.2：
Models and Distribution Assumptions / 11.3.3：
Estimation and Testing with Normal Errors / 11.3.4：
Estimation and Prediction at a Specified x = x[subscript 0] / 11.3.5：
Simultaneous Estimation and Confidence Bands / 11.3.6：
Regression Models / 11.4：
Regression with Errors in Variables / 12.1：
Functional and Structural Relationships / 12.2.1：
A Least Squares Solution / 12.2.2：
Maximum Likelihood Estimation / 12.2.3：
Confidence Sets / 12.2.4：
Logistic Regression / 12.3：
The Model / 12.3.1：
Estimation / 12.3.2：
Robust Regression / 12.4：
Computer Algebra / 12.5：
Table of Common Distributions
References
Author Index
Subject Index
Probability Theory / 1：
Set Theory / 1.1：
Basics of Probability Theory / 1.2：
4.

図書
図書
4. Spin glasses : a challenge for mathematicians : cavity and mean field models
Michel Talagrand
出版情報: Berlin ; Tokyo : Springer, c2003  ix, 586 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 46
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5.

図書
図書
5. Probability essentials. 2nd ed
Jean Jacod, Philip Protter
出版情報: Berlin ; Tokyo : Springer, c2003  x, 254 p. ; 24 cm
シリーズ名: Universitext
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Introduction / 1：
Axioms of Probability / 2：
Conditional Probability and Independence / 3：
Probabilities on a Countable Space / 4：
Random Variables on a Countable Space / 5：
Construction of a Probability Measure / 6：
Construction of a Probability Measure on R / 7：
Random Variables / 8：
Integration with Respect to a Probability Measure / 9：
Independent Random Variables / 10：
Probability Distributions on R / 11：
Probability Distributions on Rn / 12：
Characteristic Functions / 13：
Properties of Characteristic Functions / 14：
Sums of Independent Random Variables / 15：
Gaussian Random Variables (The Normal and the Multivariate Normal Distributions) / 16：
Convergence of Random Variables / 17：
Weak Convergence / 18：
Weak Convergence and Characteristic Functions / 19：
The Laws of Large Numbers / 20：
The Central Limit Theorem / 21：
L2 and Hilbert Spaces / 22：
Conditional Expectation / 23：
Martingales / 24：
Supermartingales and Submartingales / 25：
Martingale Inequalities / 26：
Martingales Convergence Theorems / 27：
The Radon-Nikodym Theorem / 28：
Introduction / 1：
Axioms of Probability / 2：
Conditional Probability and Independence / 3：
6.

図書
図書
6. Gian-Carlo Rota on analysis and probability : selected papers and commentaries (: Boston ; : Basel)
Jean Dhombres, Joseph P.S. Kung, Norton Starr, editors
出版情報: Boston ; Basel : Birkhäuser, c2003  xxx, 381 p. ; 26 cm
シリーズ名: Contemporary mathematicians
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Contributors
Editors' Preface
List of Reprinted Papers in Chronological Order
Gian-Carlo Rota on His Work in Analysis
Reminiscences of Gian-Carlo Rota / P. Duren
Gian-Carlo Rota (1932-1999) / J.T. Schwartz
Acknowledgements
Differential Operators
Theory of Linear Operators
Reynolds Operators
Ergodic Theory
Inequalities
Geometric Probability and Profinite Combinatorics
Probability Theory
Contributors
Editors' Preface
List of Reprinted Papers in Chronological Order
7.

図書
図書
7. Foundations of modern probability. 2nd ed
Olav Kallenberg
出版情報: New York ; Tokyo : Springer, c2002  xvii, 638 p. ; 24 cm
シリーズ名: Probability and its applications
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8.

図書
図書
8. Probability models
John Haigh
出版情報: London ; Berlin : Springer, c2002  viii, 256 p. ; 24 cm
シリーズ名: Springer undergraduate mathematics series
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9.

図書
図書
9. Analysis in integer and fractional dimensions (: hbk.)
Ron Blei
出版情報: Cambridge, [Eng.] ; New York : Cambridge University Press, 2001  xix, 556 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 71
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Preface
A prologue: mostly historical / 1：
Three classical inequalities / 2：
A fourth inequality / 3：
Elementary properties of the Frechet variation - an introduction to tensor products / 4：
The Grothendieck factorization theorem / 5：
An introduction to multidimensional measure theory / 6：
An introduction to harmonic analysis / 7：
Multilinear extensions of the Grothendieck inequality / 8：
Product Frechet measures / 9：
Brownian motion and the Wiener process / 10：
Integrator / 11：
A '3/2n- dimensional' Cartesian product / 12：
Fractional Cartesian products and combinatorial dimension / 13：
The last chapter: leads and loose ends / 14：
Preface
A prologue: mostly historical / 1：
Three classical inequalities / 2：
10.

図書
図書
10. Probability : elements of the mathematical theory (pbk.)
C.R. Heathcote
出版情報: Mineola, N.Y. : Dover Publications, 2000  267 p. ; 22 cm
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11.

図書
図書
11. Introduction to Probability
Dimitri P. Bertsekas and John N. Tsitsiklis
出版情報: Belmont, Mass. : Athena Scientific, c2002  ix, 416 p. ; 25 cm
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12.

図書
図書
12. Real analysis and probability (: hbk ; : pbk)
R.M. Dudley
出版情報: Cambridge : Cambridge University Press, 2002  x, 555 p. ; 23 cm
シリーズ名: Cambridge studies in advanced mathematics ; 74
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Foundations: set theory / 1：
General topology / 2：
Measures / 3：
Integration / 4：
Lp spaces: introduction to functional analysis / 5：
Convex sets and duality of normed spaces / 6：
Measure, topology, and differentiation / 7：
Introduction to probability theory / 8：
Convergence of laws and central limit theorems / 9：
Conditional expectations and martingales / 10：
Convergence of laws on separable metric spaces / 11：
Stochastic processes / 12：
Measurability: Borel isomorphism and analytic sets / 13：
Appendixes
Axiomatic set theory / A：
Complex numbers, vector spaces, and Taylor's theorem with remainder
The problem of measure
Rearranging sums of nonnegative terms
Pathologies of compact nonmetric spaces
Indices
Foundations: set theory / 1：
General topology / 2：
Measures / 3：
13.

図書
図書
13. Introduction to probability models. 9th ed
Sheldon M. Ross
出版情報: Amsterdam ; San Diego, Calif. ; Tokyo : Academic Press, c2007  xviii, 782 p. ; 24 cm
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Preface
Introduction to Probability Theory / 1：
Random Variables / 2：
Conditional Probability and Conditional Expectation / 3：
Markov Chains / 4：
The Exponential Distribution and the Poisson Process / 5：
Continuous-Time Markov Chains / 6：
Renewal Theory and Its Applications / 7：
Queueing Theory / 8：
Reliability Theory / 9：
Brownian Motion and Stationary Processes / 10：
Simulation / 11：
Appendix: Solutions to Starred Exercises
Index
Preface
Introduction to Probability Theory / 1：
Random Variables / 2：
14.

図書
図書
14. Elements of applied probability for engineering, mathematics and systems science
David McDonald
出版情報: New Jersey : World Scientific, c2004  xiii, 361 p. ; 26 cm
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15.

図書
図書
15. Recent advances in applied probability (:hb ; :e-book)
edited by Ricardo Baeza-Yates ... [et al.]
出版情報: New York : Springer, c2005  xii, 497 p. ; 25 cm
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Modeling Text Databases.
An Overview of Probabilistic and Time Series Models in Finance.
Stereological Estimation of the Rose of Directions.
Approximations for Multiple Scan Statistics.
Krawtchouk Polynomials and Krawtchouk Matrices.
An Elementary Rigorous Introduction to Exact Sampling.
On the Different Extensions of the Ergodic Theorem of Information Theory.
Dynamic Stochastic Models for Indexes and Thesauri.
Stability and Optimal Control.
Statistical Distances Based on Euclidean Graphs.
Implied Volatility.
On the Increments of the Brownian Sheet.
Compound Poisson Approximation.
Penalized Model Selection for Ill-posed Linear Problems.
The Arov-Grossman Model.
Recent Results in Geometric Analysis.
Dependence or Independence of the Sample Mean.
Optimal Stopping Problems for Time-Homogeneous Diffusions.
Criticality in Epidemics.
Acknowledgments.
Reference.
Index.
Modeling Text Databases.
An Overview of Probabilistic and Time Series Models in Finance.
Stereological Estimation of the Rose of Directions.
16.

図書
図書
16. Chance & choice : memorabilia
Kai Lai Chung
出版情報: New Jersey : World Scientific, c2004  ix, 304 p., [12] p. of plates ; 26 cm
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17.

図書
図書
17. Inference for change-point and post-change means after a CUSUM test
Yanhong Wu
出版情報: New York, N.Y. : Springer, c2005  xiii, 158 p. ; 24 cm
シリーズ名: Lecture notes in statistics ; 180
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CUSUM Procedure
Change-point Estimation
Confidence Interval for Change-point
Infrence for Post-change Mean
Estimation After False Signal
Inference with Change in Variance
Sequential Classification and Segmentation
An Adaptive CUSUM Procedure
Dependent Observation Case
Other Methods and Remarks
CUSUM Procedure
Change-point Estimation
Confidence Interval for Change-point
18.

図書
図書
18. An introduction to measure-theoretic probability
George G. Roussas
出版情報: Amsterdam ; Tokyo : Elsevier Academic Press, c2005  xviii, 443 p. ; 24 cm
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Preface
Certain Classes of Sets, Measurability, Pointwise Approximation / 1：
Definition and Construction of a Measure and Its Basic Properties / 2：
Some Modes of Convergence of a Sequence of Random Variables and Their Relationships / 3：
The Integral of a Random Variable and Its Basic Properties / 4：
Standard Convergence Theorems, The Fubini Theorem / 5：
Standard Moment and Probability Inequalities, Convergence in the r-th Mean and Its Implications / 6：
The Hahn-Jordan Decomposition Theorem, The Lebesgue Decomposition Theorem, and The Radon-Nikcodym Theorem / 7：
Distribution Functions and Their Basic Properties, Helly-Bray Type Results / 8：
Conditional Expectation and Conditional Probability, and Related Properties and Results / 9：
Independence / 10：
Topics from the Theory of Characteristic Functions / 11：
The Central Limit Problem: The Centered Case / 12：
The Central Limit Problem: The Noncentered Case / 13：
Topics from Sequences of Independent Random Variables / 14：
Topics from Ergodic Theory / 15：
Preface
Certain Classes of Sets, Measurability, Pointwise Approximation / 1：
Definition and Construction of a Measure and Its Basic Properties / 2：
19.

図書
図書
19. Probability theory
S.R.S. Varadhan
出版情報: New York : Courant Institute of Mathematical Sciences , Providence, RI. : American Mathematical Society, c2001  vii, 167 p. ; 26 cm
シリーズ名: Courant lecture notes in mathematics ; 7
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Measure theory Weak convergence Independent sums Dependent random variables Martingales
Stationary stochastic processes Dynamic programming and filtering
Bibliography
Index
Measure theory Weak convergence Independent sums Dependent random variables Martingales
Stationary stochastic processes Dynamic programming and filtering
Bibliography
20.

図書
図書
20. Basic probability theory with applications
Mario Lefebvre
出版情報: New York : Springer, c2009  xvi, 340 p. ; 25 cm
シリーズ名: Springer undergraduate texts in mathematics and technology
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Preface
List of Tables
List of Figures
Review of differential calculus / 1：
Limits and continuity / 1.1：
Derivatives / 1.2：
Integrals / 1.3：
Particular integration techniques / 1.3.1：
Double integrals / 1.3.2：
Infinite series / 1.4：
Geometric series / 1.4.1：
Exercises for Chapter 1 / 1.5：
Elementary probability / 2：
Random experiments / 2.1：
Events / 2.2：
Probability / 2.3：
Conditional probability / 2.4：
Total probability / 2.5：
Combinatorial analysis / 2.6：
Exercises for Chapter 2 / 2.7：
Random variables / 3：
Introduction / 3.1：
Discrete case / 3.1.1：
Continuous case / 3.1.2：
Important discrete random variables / 3.2：
Binomial distribution / 3.2.1：
Geometric and negative binomial distributions / 3.2.2：
Hypergeometric distribution / 3.2.3：
Poisson distribution and process / 3.2.4：
Important continuous random variables / 3.3：
Normal distribution / 3.3.1：
Gamma distribution / 3.3.2：
Weibull distribution / 3.3.3：
Beta distribution / 3.3.4：
Lognormal distribution / 3.3.5：
Functions of Random variables / 3.4：
Characteristics of random variables / 3.4.1：
Exercises for Chapter 3 / 3.6：
Random vectors / 4：
Discrete random vectors / 4.1：
Continuous random vectors / 4.2：
Functions of random vectors / 4.3：
Convolutions / 4.3.1：
Covariance and correlation coefficient / 4.4：
Limit theorems / 4.5：
Exercises for Chapter 4 / 4.6：
Reliability / 5：
Basic notions / 5.1：
Reliability of systems / 5.2：
Systems in series / 5.2.1：
Systems in parallel / 5.2.2：
Other cases / 5.2.3：
Paths and cuts / 5.3：
Exercises for Chapter 5 / 5.4：
Queueing / 6：
Continuous-time Markov chains / 6.1：
Quening systems with a single server / 6.2：
The M/M/1 model / 6.2.1：
The M/M/1 model with finite capacity / 6.2.2：
Queueing systems with two or more servers / 6.3：
The M/M/s model / 6.3.1：
The M/M/s/c model / 6.3.2：
Exercises for Chapter 6 / 6.4：
Time series / 7：
Particular time series models / 7.1：
Autoregressive processes / 7.2.1：
Moving average processes / 7.2.2：
Autoregressive moving average processes / 7.2.3：
Modeling and forecasting / 7.3：
Exercises for Chapter 7 / 7.4：
List of symbols and abbreviations / A：
Statistical tables / B：
Solutions to "Solved exercises" / C：
Answers to even-numbered exercises / D：
Answers to multiple choice questions / E：
References
Index
Preface
List of Tables
List of Figures
21.

図書
図書
21. Stochastic finance : an introduction in discrete time
Hans Föllmer, Alexander Schied
出版情報: Berlin : W. de Gruyter, 2002  ix, 422 p. ; 25 cm
シリーズ名: De Gruyter studies in mathematics ; 27
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Introduction
Mathematical finance in one period / I：
Arbitrage theory / 1：
Assets, portfolios, and arbitrage opportunities / 1.1：
Absence of arbitrage and martingale measures / 1.2：
Derivative securities / 1.3：
Complete market models / 1.4：
Geometric characterization of arbitrage-free models / 1.5：
Contingent initial data / 1.6：
Preferences / 2：
Preference relations and their numerical representation / 2.1：
Von Neumann-Morgenstern representation / 2.2：
Expected utility / 2.3：
Uniform preferences / 2.4：
Robust preferences on asset profiles / 2.5：
Probability measures with given marginals / 2.6：
Optimality and equilibrium / 3：
Portfolio optimization and the absence of arbitrage / 3.1：
Exponential utility and relative entropy / 3.2：
Optimal contingent claims / 3.3：
Microeconomic equilibrium / 3.4：
Monetary measures of risk / 4：
Risk measures and their acceptance sets / 4.1：
Robust representation of convex risk measures / 4.2：
Convex risk measures on L[infinity] / 4.3：
Value at Risk / 4.4：
Measures of risk in a financial market / 4.5：
Shortfall risk / 4.6：
Dynamic hedging / II：
Dynamic arbitrage theory / 5：
The multi-period market model / 5.1：
Arbitrage opportunities and martingale measures / 5.2：
European contingent claims / 5.3：
Complete markets / 5.4：
The binomial model / 5.5：
Convergence to the Black-Scholes price / 5.6：
American contingent claims / 6：
Hedging strategies for the seller / 6.1：
Stopping strategies for the buyer / 6.2：
Arbitrage-free prices / 6.3：
Lower Snell envelopes / 6.4：
Superhedging / 7：
P-supermartingales and upper Snell envelopes / 7.1：
Uniform Doob decomposition / 7.2：
Superhedging of American and European claims / 7.3：
Superhedging with derivatives / 7.4：
Efficient hedging / 8：
Quantile hedging / 8.1：
Hedging with minimal shortfall risk / 8.2：
Hedging under constraints / 9：
Absence of arbitrage opportunities / 9.1：
Upper Snell envelopes / 9.2：
Superhedging and risk measures / 9.4：
Minimizing the hedging error / 10：
Local quadratic risk / 10.1：
Minimal martingale measures / 10.2：
Variance-optimal hedging / 10.3：
Appendix
Convexity / A.1：
Absolutely continuous probability measures / A.2：
The Neyman-Pearson lemma / A.3：
The essential supremum of a family of random variables / A.4：
Spaces of measures / A.5：
Some functional analysis / A.6：
Introduction
Mathematical finance in one period / I：
Arbitrage theory / 1：
22.

図書
図書
22. Probabilistic robotics
Sebastian Thrun, Wolfram Burgard, Dieter Fox
出版情報: Cambridge, Mass. : MIT Press, c2006  xx, 647 p. ; 24 cm
シリーズ名: Intelligent robotics and autonomous agents
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Preface
Acknowledgments
Basics / I：
Introduction / 1：
Uncertainty in Robotics / 1.1：
Probabilistic Robotics / 1.2：
Implications / 1.3：
Road Map / 1.4：
Teaching Probabilistic Robotics / 1.5：
Bibliographical Remarks / 1.6：
Recursive State Estimation / 2：
Basic Concepts in Probability / 2.1：
Robot Environment Interaction / 2.3：
Bayes Filters / 2.4：
Representation and Computation / 2.5：
Summary / 2.6：
Exercises / 2.7：
Gaussian Filters / 3：
The Kalman Filter / 3.1：
The Extended Kalman Filter / 3.3：
The Unscented Kalman Filter / 3.4：
The Information Filter / 3.5：
Nonparametric Filters / 3.6：
The Histogram Filter / 4.1：
Binary Bayes Filters with Static State / 4.2：
The Particle Filter / 4.3：
Robot Motion / 4.4：
Preliminaries / 5.1：
Velocity Motion Model / 5.3：
Odometry Motion Model / 5.4：
Motion and Maps / 5.5：
Robot Perception / 5.6：
Maps / 6.1：
Beam Models of Range Finders / 6.3：
Likelihood Fields for Range Finders / 6.4：
Correlation-Based Measurement Models / 6.5：
Feature-Based Measurement Models / 6.6：
Practical Considerations / 6.7：
Localization / 6.8：
Mobile Robot Localization: Markov and Gaussian / 7：
A Taxonomy of Localization Problems / 7.1：
Markov Localization / 7.2：
Illustration of Markov Localization / 7.3：
EKF Localization / 7.4：
Estimating Correspondences / 7.5：
Multi-Hypothesis Tracking / 7.6：
UKF Localization / 7.7：
Mobile Robot Localization: Grid And Monte Carlo / 7.8：
Grid Localization / 8.1：
Monte Carlo Localization / 8.3：
Localization in Dynamic Environments / 8.4：
Mapping / 8.5：
Occupancy Grid Mapping / 9：
The Occupancy Grid Mapping Algorithm / 9.1：
Learning Inverse Measurement Models / 9.3：
Maximum A Posteriori Occupancy Mapping / 9.4：
Simultaneous Localization and Mapping / 9.5：
SLAM with Extended Kalman Filters / 10.1：
EKF SLAM with Unknown Correspondences / 10.3：
The GraphSLAM Algorithm / 10.4：
Intuitive Description / 11.1：
Mathematical Derivation of GraphSLAM / 11.3：
Data Association in GraphSLAM / 11.5：
Efficiency Consideration / 11.6：
Empirical Implementation / 11.7：
Alternative Optimization Techniques / 11.8：
The Sparse Extended Information Filter / 11.9：
The SEIF SLAM Algorithm / 12.1：
Mathematical Derivation of the SEIF / 12.4：
Sparsification / 12.5：
Amortized Approximate Map Recovery / 12.6：
How Sparse Should SEIFs Be? / 12.7：
Incremental Data Association / 12.8：
Branch-and-Bound Data Association / 12.9：
Multi-Robot SLAM / 12.10：
The FastSLAM Algorithm / 12.12：
The Basic Algorithm / 13.1：
Factoring the SLAM Posterior / 13.2：
FastSLAM with Known Data Association / 13.3：
Improving the Proposal Distribution / 13.4：
Unknown Data Association / 13.5：
Map Management / 13.6：
The FastSLAM Algorithms / 13.7：
Efficient Implementation / 13.8：
FastSLAM for Feature-Based Maps / 13.9：
Grid-based FastSLAM / 13.10：
Planning and Control / 13.11：
Markov Decision Processes / 14：
Motivation / 14.1：
Uncertainty in Action Selection / 14.2：
Value Iteration / 14.3：
Application to Robot Control / 14.4：
Partially Observable Markov Decision Processes / 14.5：
An Illustrative Example / 15.1：
The Finite World POMDP Algorithm / 15.3：
Mathematical Derivation of POMDPs / 15.4：
Approximate POMDP Techniques / 15.5：
QMDPs / 16.1：
Augmented Markov Decision Processes / 16.3：
Monte Carlo POMDPs / 16.4：
Exploration / 16.5：
Basic Exploration Algorithms / 17.1：
Active Localization / 17.3：
Exploration for Learning Occupancy Grid Maps / 17.4：
Exploration for SLAM / 17.5：
Bibliography / 17.6：
Index
Preface
Acknowledgments
Basics / I：
23.

図書
図書
23. A first look at rigorous probability theory. 2nd ed (: [hd.] ; : pbk)
Jeffrey S. Rosenthal
出版情報: Singapore ; New Jersey : World Scientific, c2006  xvi, 219 p. ; 24 cm
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Preface to the First Edition
Preface to the Second Edition
The need for measure theory / 1：
Various kinds of random variables / 1.1：
The uniform distribution and non-measurable sets / 1.2：
Exercises / 1.3：
Section summary / 1.4：
Probability triples / 2：
Basic definition / 2.1：
Constructing probability triples / 2.2：
The Extension Theorem / 2.3：
Constructing the Uniform[0,1] distribution / 2.4：
Extensions of the Extension Theorem / 2.5：
Coin tossing and other measures / 2.6：
Further probabilistic foundations / 2.7：
Random variables / 3.1：
Independence / 3.2：
Continuity of probabilities / 3.3：
Limit events / 3.4：
Tail fields / 3.5：
Expected values / 3.6：
Simple random variables / 4.1：
General non-negative random variables / 4.2：
Arbitrary random variables / 4.3：
The integration connection / 4.4：
Inequalities and convergence / 4.5：
Various inequalities / 5.1：
Convergence of random variables / 5.2：
Laws of large numbers / 5.3：
Eliminating the moment conditions / 5.4：
Distributions of random variables / 5.5：
Change of variable theorem / 6.1：
Examples of distributions / 6.2：
Stochastic processes and gambling games / 6.3：
A first existence theorem / 7.1：
Gambling and gambler's ruin / 7.2：
Gambling policies / 7.3：
Discrete Markov chains / 7.4：
A Markov chain existence theorem / 8.1：
Transience, recurrence, and irreducibility / 8.2：
Stationary distributions and convergence / 8.3：
Existence of stationary distributions / 8.4：
More probability theorems / 8.5：
Limit theorems / 9.1：
Differentiation of expectation / 9.2：
Moment generating functions and large deviations / 9.3：
Fubini's Theorem and convolution / 9.4：
Weak convergence / 9.5：
Equivalences of weak convergence / 10.1：
Connections to other convergence / 10.2：
Characteristic functions / 10.3：
The continuity theorem / 11.1：
The Central Limit Theorem / 11.2：
Generalisations of the Central Limit Theorem / 11.3：
Method of moments / 11.4：
Decomposition of probability laws / 11.5：
Lebesgue and Hahn decompositions / 12.1：
Decomposition with general measures / 12.2：
Conditional probability and expectation / 12.3：
Conditioning on a random variable / 13.1：
Conditioning on a sub-[sigma]-algebra / 13.2：
Conditional variance / 13.3：
Martingales / 13.4：
Stopping times / 14.1：
Martingale convergence / 14.2：
Maximal inequality / 14.3：
General stochastic processes / 14.4：
Kolmogorov Existence Theorem / 15.1：
Markov chains on general state spaces / 15.2：
Continuous-time Markov processes / 15.3：
Brownian motion as a limit / 15.4：
Existence of Brownian motion / 15.5：
Diffusions and stochastic integrals / 15.6：
Ito's Lemma / 15.7：
The Black-Scholes equation / 15.8：
Mathematical Background / 15.9：
Sets and functions / A.1：
Countable sets / A.2：
Epsilons and Limits / A.3：
Infimums and supremums / A.4：
Equivalence relations / A.5：
Bibliography / B：
Background in real analysis / B.1：
Undergraduate-level probability / B.2：
Graduate-level probability / B.3：
Pure measure theory / B.4：
Stochastic processes / B.5：
Mathematical finance / B.6：
Index
Constructing the Uniform[0, 1] distribution
Preface to the First Edition
Preface to the Second Edition
The need for measure theory / 1：
24.

図書
図書
24. Stochastic finance : an introduction in discrete time. 2nd rev. and extended ed
Hans Föllmer, Alexander Schied
出版情報: New York : Walter de Gruyter, c2004  xi, 459 p. ; 25 cm
シリーズ名: De Gruyter studies in mathematics ; 27
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25.

図書
図書
25. Optimal transport : old and new
Cédric Villani
出版情報: Berlin : Springer, c2009  xxii, 973 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; v. 338
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Preface
Conventions
Introduction
Couplings and changes of variables / 1：
Three examples of coupling techniques / 2：
The founding fathers of optimal transport / 3：
Qualitative description of optimal transport / Part I：
Basic properties / 4：
Cyclical monotonicity and Kantorovich duality / 5：
The Wasserstein distances / 6：
Displacement interpolation / 7：
The Monge-Mather shortening principle / 8：
Solution of the Monge problem I: Global approach / 9：
Solution of the Monge problem II: Local approach / 10：
The Jacobian equation / 11：
Smoothness / 12：
Qualitative picture / 13：
Optimal transport and Riemannian geometry / Part II：
Ricci curvature / 14：
Otto calculus / 15：
Displacement convexity I / 16：
Displacement convexity II / 17：
Volume control / 18：
Density control and local regularity / 19：
Infinitesimal displacement convexity / 20：
Isoperimetric-type inequalities / 21：
Concentration inequalities / 22：
Gradient flows I / 23：
Gradient flows II: Qualitative properties / 24：
Gradient flows III: Functional inequalities / 25：
Synthetic treatment of Ricci curvature / Part III：
Analytic and synthetic points of view / 26：
Convergence of metric-measure spaces / 27：
Stability of optimal transport / 28：
Weak Ricci curvature bounds I: Definition and Stability / 29：
Weak Ricci curvature bounds II: Geometric and analytic properties / 30：
Conclusions and open problems
References
List of short statements
List of figures
Index
Some notable cost functions
Preface
Conventions
Introduction
26.

電子ブック
ＥＢ
26. A course in probability theory. 3rd ed (: electronic bk)
Kai Lai Chung
出版情報: San Diego ; Tokyo : Academic Press, c2001  1 online resource (xvi, 419 p. ; 23 cm)
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Preface to the third edition
Preface to the second edition
Preface to the first edition
Distribution function / 1：
Monotone functions / 1.1：
Distribution functions / 1.2：
Absolutely continuous and singular distributions / 1.3：
Measure theory / 2：
Classes of sets / 2.1：
Probability measures and their distribution functions / 2.2：
Random variable. Expectation. Independence / 3：
General definitions / 3.1：
Properties of mathematical expectation / 3.2：
Independence / 3.3：
Convergence concepts / 4：
Various modes of convergence / 4.1：
Almost sure convergence; Borel-Cantelli lemma / 4.2：
Vague convergence / 4.3：
Continuation / 4.4：
Uniform integrability; convergence of moments / 4.5：
Law of large numbers. Random series / 5：
Simple limit theorems / 5.1：
Weak law of large numbers / 5.2：
Convergence of series / 5.3：
Strong law of large numbers / 5.4：
Applications / 5.5：
Bibliographical Note
Characteristic function / 6：
General properties; convolutions / 6.1：
Uniqueness and inversion / 6.2：
Convergence theorems / 6.3：
Simple applications / 6.4：
Representation theorems / 6.5：
Multidimensional case; Laplace transforms / 6.6：
Central limit theorem and its ramifications / 7：
Liapounov's theorem / 7.1：
Lindeberg-Feller theorem / 7.2：
Ramifications of the central limit theorem / 7.3：
Error estimation / 7.4：
Law of the iterated logarithm / 7.5：
Infinite divisibility / 7.6：
Random walk / 8：
Zero-or-one laws / 8.1：
Basic notions / 8.2：
Recurrence / 8.3：
Fine structure / 8.4：
Conditioning. Markov property. Martingale / 8.5：
Basic properties of conditional expectation / 9.1：
Conditional independence; Markov property / 9.2：
Basic properties of smartingales / 9.3：
Inequalities and convergence / 9.4：
Supplement: Measure and Integral / 9.5：
Construction of measure
Characterization of extensions
Measures in R
Integral
General Bibliography
Index
Preface to the third edition
Preface to the second edition
Preface to the first edition
27.

電子ブック
ＥＢ
27. The Arrow impossibility theorem (: electronic bk)
Eric Maskin, Amartya Sen ; with Kenneth J. Arrow ... [et al.]
出版情報: [S.l.] : EBSCOhost, [20--]  1 online resource (vi, 152 p.)
シリーズ名: Kenneth J. Arrow lecture series ;
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28.

電子ブック
ＥＢ
28. Measure, integral, and probability (: electronic bk)
Marek Capiński and Ekkehard Kopp
出版情報: London : Springer, [20--]  1 online resource (xi, 227 p.)
シリーズ名: Springer undergraduate mathematics series
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Motivation and preliminaries / 1：
Notation and basic set theory / 1.1：
Sets and functions / 1.1.1：
Countable and uncountable sets in <$>\cal {R}<$> / 1.1.2：
Topological properties of sets in <$>\cal {R}<$> / 1.1.3：
The Riemann integral: scope and limitations / 1.2：
Choosing numbers at random / 1.3：
Measure / 2：
Null sets / 2.1：
Outer measure / 2.2：
Lebesgue measurable sets and Lebesgue measure / 2.3：
Basic properties of Lebesgue measure / 2.4：
Borel sets / 2.5：
Probability / 2.6：
Probability space / 2.6.1：
Events: conditioning and independence / 2.6.2：
Proofs of propositions / 2.7：
Measurable functions / 3：
The extended real line / 3.1：
Definition / 3.2：
Examples / 3.3：
Properties / 3.4：
Random variables / 3.5：
Sigma fields generated by random variables / 3.5.2：
Probability distributions / 3.5.3：
Independence of random variables / 3.5.4：
Integral / 3.6：
Definition of the integral / 4.1：
Monotone Convergence Theorems / 4.2：
Integrable functions / 4.3：
The Dominated Convergence Theorem / 4.4：
Relation to the Riemann integral / 4.5：
Approximation of measurable functions / 4.6：
Integration with respect to probability distributions / 4.7：
Absolutely continuous measures: examples of densities / 4.7.2：
Expectation of a random variable / 4.7.3：
Characteristic function / 4.7.4：
Spaces of integrable functions / 4.8：
The space L1 / 5.1：
The Hilbert space L2 / 5.2：
Properties of the L2-norm / 5.2.1：
Inner product spaces / 5.2.2：
Orthogonality / 5.2.3：
The Lp spaces: completeness / 5.3：
Moments / 5.4：
Independence / 5.4.2：
Product measures / 5.5：
Multi-dimensional Lebesgue measure / 6.1：
Product σ-fields / 6.2：
Construction of the product measure / 6.3：
Fubini's Theorem / 6.4：
Joint distributions / 6.5：
Independence again / 6.5.2：
Conditional probability / 6.5.3：
Characteristic functions determine distributions / 6.5.4：
Limit theorems / 6.6：
Modes of convergence / 7.1：
Convergence in probability / 7.2：
Weak law of large numbers / 7.2.2：
Borel-Cantelli lemmas / 7.2.3：
Strong law of large numbers / 7.2.4：
Weak convergence / 7.2.5：
Central Limit Theorem / 7.2.6：
Solutions to exercises / 7.3：
Appendix / 9：
References
Index
Motivation and preliminaries / 1：
Notation and basic set theory / 1.1：
Sets and functions / 1.1.1：
29.

電子ブック
ＥＢ
29. Introduction to empirical processes and semiparametric inference (: electronic bk)
Michael R. Kosorok
出版情報: [Berlin] : SpringerLink, [20--]  1 online resource (xiv, 483 p.)
シリーズ名: Springer series in statistics
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Preface
Overview / I：
Introduction / 1：
An Overview of Empirical Processes / 2：
The Main Features / 2.1：
Empirical Process Techniques / 2.2：
Stochastic Convergence / 2.2.1：
Entropy for Glivenko-Cantelli and Donsker Theorems / 2.2.2：
Bootstrapping Empirical Processes / 2.2.3：
The Functional Delta Method / 2.2.4：
Z-Estimators / 2.2.5：
M-Estimators / 2.2.6：
Other Topics / 2.3：
Exercises / 2.4：
Notes / 2.5：
Overview of Semiparametric Inference / 3：
Semiparametric Models and Efficiency / 3.1：
Score Functions and Estimating Equations / 3.2：
Maximum Likelihood Estimation / 3.3：
Case Studies I / 3.4：
Linear Regression / 4.1：
Mean Zero Residuals / 4.1.1：
Median Zero Residuals / 4.1.2：
Counting Process Regression / 4.2：
The General Case / 4.2.1：
The Cox Model / 4.2.2：
The Kaplan-Meier Estimator / 4.3：
Efficient Estimating Equations for Regression / 4.4：
Simple Linear Regression / 4.4.1：
A Poisson Mixture Regression Model / 4.4.2：
Partly Linear Logistic Regression / 4.5：
Empirical Processes / 4.6：
Introduction to Empirical Processes / 5：
Preliminaries for Empirical Processes / 6：
Metric Spaces / 6.1：
Outer Expectation / 6.2：
Linear Operators and Functional Differentiation / 6.3：
Proofs / 6.4：
Stochastic Processes in Metric Spaces / 6.5：
Weak Convergence / 7.2：
General Theory / 7.2.1：
Spaces of Bounded Functions / 7.2.2：
Other Modes of Convergence / 7.3：
Empirical Process Methods / 7.4：
Maximal Inequalities / 8.1：
Orlicz Norms and Maxima / 8.1.1：
Maximal Inequalities for Processes / 8.1.2：
The Symmetrization Inequality and Measurability / 8.2：
Glivenko-Cantelli Results / 8.3：
Donsker Results / 8.4：
Entropy Calculations / 8.5：
Uniform Entropy / 9.1：
VC-Classes / 9.1.1：
BUEI Classes / 9.1.2：
Bracketing Entropy / 9.2：
Glivenko-Cantelli Preservation / 9.3：
Donsker Preservation / 9.4：
The Bootstrap for Donsker Classes / 9.5：
An Unconditional Multiplier Central Limit Theorem / 10.1.1：
Conditional Multiplier Central Limit Theorems / 10.1.2：
Bootstrap Central Limit Theorems / 10.1.3：
Continuous Mapping Results / 10.1.4：
The Bootstrap for Glivenko-Cantelli Classes / 10.2：
A Simple Z-Estimator Master Theorem / 10.3：
Additional Empirical Process Results / 10.4：
Bounding Moments and Tail Probabilities / 11.1：
Sequences of Functions / 11.2：
Contiguous Alternatives / 11.3：
Sums of Independent but not Identically Distributed Stochastic Processes / 11.4：
Central Limit Theorems / 11.4.1：
Bootstrap Results / 11.4.2：
Function Classes Changing with n / 11.5：
Dependent Observations / 11.6：
Main Results and Proofs / 11.7：
Examples / 12.2：
Composition / 12.2.1：
Integration / 12.2.2：
Product Integration / 12.2.3：
Inversion / 12.2.4：
Other Mappings / 12.2.5：
Consistency / 12.3：
The General Setting / 13.2：
Using Donsker Classes / 13.2.2：
A Master Theorem and the Bootstrap / 13.2.3：
Using the Delta Method / 13.3：
The Argmax Theorem / 13.4：
Rate of Convergence / 14.2：
Regular Euclidean M-Estimators / 14.4：
Non-Regular Examples / 14.5：
A Change-Point Model / 14.5.1：
Monotone Density Estimation / 14.5.2：
Case Studies II / 14.6：
Partly Linear Logistic Regression Revisited / 15.1：
The Two-Parameter Cox Score Process / 15.2：
The Proportional Odds Model Under Right Censoring / 15.3：
Nonparametric Maximum Likelihood Estimation / 15.3.1：
Existence / 15.3.2：
Score and Information Operators / 15.3.3：
Weak Convergence and Bootstrap Validity / 15.3.5：
Testing for a Change-point / 15.4：
Large p Small n Asymptotics for Microarrays / 15.5：
Assessing P-Value Approximations / 15.5.1：
Consistency of Marginal Empirical Distribution Functions / 15.5.2：
Inference for Marginal Sample Means / 15.5.3：
Semiparametric Inference / 15.6：
Introduction to Semiparametric Inference / 16：
Preliminaries for Semiparametric Inference / 17：
Projections / 17.1：
Hilbert Spaces / 17.2：
More on Banach Spaces / 17.3：
Tangent Sets and Regularity / 17.4：
Efficiency / 18.2：
Optimality of Tests / 18.3：
Efficient Inference for Finite-Dimensional Parameters / 18.4：
Efficient Score Equations / 19.1：
Profile Likelihood and Least-Favorable Submodels / 19.2：
The Cox Model for Right Censored Data / 19.2.1：
The Proportional Odds Model for Right Censored Data / 19.2.2：
The Cox Model for Current Status Data / 19.2.3：
Inference / 19.2.4：
Quadratic Expansion of the Profile Likelihood / 19.3.1：
The Profile Sampler / 19.3.2：
The Penalized Profile Sampler / 19.3.3：
Other Methods / 19.3.4：
Efficient Inference for Infinite-Dimensional Parameters / 19.4：
Semiparametric Maximum Likelihood Estimation / 20.1：
Weighted and Nonparametric Bootstraps / 20.2：
The Piggyback Bootstrap / 20.2.2：
Semiparametric M-Estimation / 20.2.3：
Semiparametric M-estimators / 21.1：
Motivating Examples / 21.1.1：
General Scheme for Semiparametric M-Estimators / 21.1.2：
Consistency and Rate of Convergence / 21.1.3：
[radical]n Consistency and Asymptotic Normality / 21.1.4：
Weighted M-Estimators and the Weighted Bootstrap / 21.2：
Entropy Control / 21.3：
Examples Continued / 21.4：
Cox Model with Current Status Data (Example 1, Continued) / 21.4.1：
Binary Regression Under Misspecified Link Function (Example 2, Continued) / 21.4.2：
Mixture Models (Example 3, Continued) / 21.4.3：
Penalized M-estimation / 21.5：
Two Other Examples / 21.5.1：
Case Studies III / 21.6：
The Proportional Odds Model Under Right Censoring Revisited / 22.1：
Efficient Linear Regression / 22.2：
Temporal Process Regression / 22.3：
A Partly Linear Model for Repeated Measures / 22.4：
References / 22.5：
Author Index
List of symbols
Subject Index
Preface
Overview / I：
Introduction / 1：
30.

図書
図書
30. Probability concepts in engineering : emphasis on applications in civil and environmental engineering. 2nd ed
Alfredo H-S. Ang, Wilson H. Tang
出版情報: New York : Wiley, c2007  xiii, 406 p. ; 27 cm
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Preface
Roles of Probability and Statistics in Engineering / Chapter 1：
Introduction / 1.1：
Uncertainty in Engineering / 1.2：
Uncertainty Associated with Randomness-The Aleatory Uncertainty / 1.2.1：
Uncertainty Associated with Imperfect Knowledge-The Epistemic Uncertainty / 1.2.2：
Design and Decision Making under Uncertainty / 1.3：
Planning and Design of Transportation Infrastructures / 1.3.1：
Design of Structures and Machines / 1.3.2：
Planning and Design of Hydrosystems / 1.3.3：
Design of Geotechnical Systems / 1.3.4：
Construction Planning and Management / 1.3.5：
Photogrammetric, Geodetic, and Surveying Measurements / 1.3.6：
Applications in Quality Control and Assurance / 1.3.7：
Concluding Summary / 1.4：
References
Fundamentals of Probability Models / Chapter 2：
Events and Probability / 2.1：
Characteristics of Problems Involving Probabilities / 2.1.1：
Estimating Probabilities / 2.1.2：
Elements of Set Theory-Tools for Defining Events / 2.2：
Important Definitions / 2.2.1：
Mathematical Operations of Sets / 2.2.2：
Mathematics of Probability / 2.3：
The Addition Rule / 2.3.1：
Conditional Probability / 2.3.2：
The Multiplication Rule / 2.3.3：
The Theorem of Total Probability / 2.3.4：
The Bayes' Theorem / 2.3.5：
Problems / 2.4：
Analytical Models of Random Phenomena / Chapter 3：
Random Variables and Probability Distribution / 3.1：
Random Events and Random Variables / 3.1.1：
Probability Distribution of a Random Variable / 3.1.2：
Main Descriptors of a Random Variable / 3.1.3：
Useful Probability Distributions / 3.2：
The Gaussian (or Normal) Distribution / 3.2.1：
The Lognormal Distribution / 3.2.2：
The Bernoulli Sequence and the Binomial Distribution / 3.2.3：
The Geometric Distribution / 3.2.4：
The Negative Binomial Distribution / 3.2.5：
The Poisson Process and the Poisson Distribution / 3.2.6：
The Exponential Distribution / 3.2.7：
The Gamma Distribution / 3.2.8：
The Hypergeometric Distribution / 3.2.9：
The Beta Distribution / 3.2.10：
Other Useful Distributions / 3.2.11：
Multiple Random Variables / 3.3：
Joint and Conditional Probability Distributions / 3.3.1：
Covariance and Correlation / 3.3.2：
Functions of Random Variables / 3.4：
Derived Probability Distributions / 4.1：
Function of a Single Random Variable / 4.2.1：
Function of Multiple Random Variables / 4.2.2：
Extreme Value Distributions / 4.2.3：
Moments of Functions of Random Variables / 4.3：
Mathematical Expectations of a Function / 4.3.1：
Mean and Variance of a General Function / 4.3.2：
Computer-Based Numerical and Simulation Methods in Probability / 4.4：
Numerical and Simulations Methods / 5.1：
Essentials of Monte Carlo Simulation / 5.2.1：
Numerical Examples / 5.2.2：
Problems Involving Aleatory and Epistemic Uncertainties / 5.2.3：
MCS Involving Correlated Random Variables / 5.2.4：
References and Softwares / 5.3：
Statistical Inferences from Observational Data / Chapter 6：
Role of Statistical Inference in Engineering / 6.1：
Statistical Estimation of Parameters / 6.2：
Random Sampling and Point Estimation / 6.2.1：
Sampling Distributions / 6.2.2：
Testing of Hypotheses / 6.3：
Hypothesis Test Procedure / 6.3.1：
Confidence Intervals / 6.4：
Confidence Interval of the Mean / 6.4.1：
Confidence Interval of the Proportion / 6.4.2：
Confidence Interval of the Variance / 6.4.3：
Measurement Theory / 6.5：
Determination of Probability Distribution Models / 6.6：
Probability Papers / 7.1：
Utility and Plotting Position / 7.2.1：
The Normal Probability Paper / 7.2.2：
The Lognormal Probability Paper / 7.2.3：
Construction of General Probability Papers / 7.2.4：
Testing Goodness-of-Fit of Distribution Models / 7.3：
The Chi-Square Test for Goodness-of-Fit / 7.3.1：
The Kolmogorov-Smirnov (K-S) Test for Goodness-of-Fit / 7.3.2：
The Anderson-Darling Test for Goodness-of-Fit / 7.3.3：
Invariance in the Asymptotic Forms of Extremal Distributions / 7.4：
Regression and Correlation Analyses / 7.5：
Fundamentals of Linear Regression Analysis / 8.1：
Regression with Constant Variance / 8.2.1：
Variance in Regression Analysis / 8.2.2：
Confidence Intervals in Regression / 8.2.3：
Correlation Analysis / 8.3：
Estimation of the Correlation Coefficient / 8.3.1：
Regression of Normal Variates / 8.3.2：
Linear Regression with Nonconstant Variance / 8.4：
Multiple Linear Regression / 8.5：
Nonlinear Regression / 8.6：
Applications of Regression Analysis in Engineering / 8.7：
The Bayesian Approach / 8.8：
Estimation of Parameters / 9.1：
Basic Concepts-The Discrete Case / 9.2：
The Continuous Case / 9.3：
General Formulation / 9.3.1：
A Special Application of the Bayesian Updating Process / 9.3.2：
Bayesian Concept in Sampling Theory / 9.4：
Sampling from Normal Populations / 9.4.1：
Error in Estimation / 9.4.3：
The Utility of Conjugate Distributions / 9.4.4：
Estimation of Two Parameters / 9.5：
Bayesian Regression and Correlation Analyses / 9.6：
Linear Regression / 9.6.1：
Updating the Regression Parameters / 9.6.2：
Elements of Quality Assurance and Acceptance Sampling / 9.6.3：
Appendices
Probability Tables / Appendix A：
Standard Normal Probabilities / Table A.1：
CDF of the Binomial Distribution / Table A.2：
Critical Values of t-Distribution at Confidence Level (1-[alpha]) = p / Table A.3：
Critical Values of the x[superscript 2] Distribution at probability Level [alpha] / Table A.4：
Critical Values of D[superscript alpha subscript n] at Significance Level [alpha] in the K-S Test / Table A.5：
Critical Values of the Anderson-Darling Goodness-of-Fit Test / Table A.6：
Combinatorial Formulas / Appendix B：
The Basic Relation / B.1：
The Binomial Coefficient / B.3：
The Multinomial Coefficient / B.4：
Stirling's Formula / B.5：
Derivation of the Poisson Distribution / Appendix C：
Index
Preface
Roles of Probability and Statistics in Engineering / Chapter 1：
Introduction / 1.1：
31.

図書
図書
31. Probability theory : a comprehensive course
Achim Klenke
出版情報: London : Springer, c2008  xii, 616 p. ; 24 cm
シリーズ名: Universitext
所蔵情報: loading…
目次情報: 続きを見る
Preface
Basic Measure Theory / 1：
Classes of Sets / 1.1：
Set Functions / 1.2：
The Measure Extension Theorem / 1.3：
Measurable Maps / 1.4：
Random Variables / 1.5：
Independence / 2：
Independence of Events / 2.1：
Independent Random Variables / 2.2：
Kolmogorov's 0-1 Law / 2.3：
Example: Percolation / 2.4：
Generating Functions / 3：
Definition and Examples / 3.1：
Poisson Approximation / 3.2：
Branching Processes / 3.3：
The Integral / 4：
Construction and Simple Properties / 4.1：
Monotone Convergence and Fatou's Lemma / 4.2：
Lebesgue Integral versus Riemann Integral / 4.3：
Moments and Laws of Large Numbers / 5：
Moments / 5.1：
Weak Law of Large Numbers / 5.2：
Strong Law of Large Numbers / 5.3：
Speed of Convergence in the Strong LLN / 5.4：
The Poisson Process / 5.5：
Convergence Theorems / 6：
Almost Sure and Measure Convergence / 6.1：
Uniform Integrability / 6.2：
Exchanging Integral and Differentiation / 6.3：
L[superscript p]-Spaces and the Radon-Nikodym Theorem / 7：
Definitions / 7.1：
Inequalities and the Fischer-Riesz Theorem / 7.2：
Hilbert Spaces / 7.3：
Lebesgue's Decomposition Theorem / 7.4：
Supplement: Signed Measures / 7.5：
Supplement: Dual Spaces / 7.6：
Conditional Expectations / 8：
Elementary Conditional Probabilities / 8.1：
Regular Conditional Distribution / 8.2：
Martingales / 9：
Processes, Filtrations, Stopping Times / 9.1：
Discrete Stochastic Integral / 9.2：
Discrete Martingale Representation Theorem and the CRR Model / 9.4：
Optional Sampling Theorems / 10：
Doob Decomposition and Square Variation / 10.1：
Optional Sampling and Optional Stopping / 10.2：
Uniform Integrability and Optional Sampling / 10.3：
Martingale Convergence Theorems and Their Applications / 11：
Doob's Inequality / 11.1：
Martingale Convergence Theorems / 11.2：
Example: Branching Process / 11.3：
Backwards Martingales and Exchangeability / 12：
Exchangeable Families of Random Variables / 12.1：
Backwards Martingales / 12.2：
De Finetti's Theorem / 12.3：
Convergence of Measures / 13：
A Topology Primer / 13.1：
Weak and Vague Convergence / 13.2：
Prohorov's Theorem / 13.3：
Application: A Fresh Look at de Finetti's Theorem / 13.4：
Probability Measures on Product Spaces / 14：
Product Spaces / 14.1：
Finite Products and Transition Kernels / 14.2：
Kolmogorov's Extension Theorem / 14.3：
Markov Semigroups / 14.4：
Characteristic Functions and the Central Limit Theorem / 15：
Separating Classes of Functions / 15.1：
Characteristic Functions: Examples / 15.2：
Levy's Continuity Theorem / 15.3：
Characteristic Functions and Moments / 15.4：
The Central Limit Theorem / 15.5：
Multidimensional Central Limit Theorem / 15.6：
Infinitely Divisible Distributions / 16：
Levy-Khinchin Formula / 16.1：
Stable Distributions / 16.2：
Markov Chains / 17：
Definitions and Construction / 17.1：
Discrete Markov Chains: Examples / 17.2：
Discrete Markov Processes in Continuous Time / 17.3：
Discrete Markov Chains: Recurrence and Transience / 17.4：
Application: Recurrence and Transience of Random Walks / 17.5：
Invariant Distributions / 17.6：
Convergence of Markov Chains / 18：
Periodicity of Markov Chains / 18.1：
Coupling and Convergence Theorem / 18.2：
Markov Chain Monte Carlo Method / 18.3：
Speed of Convergence / 18.4：
Markov Chains and Electrical Networks / 19：
Harmonic Functions / 19.1：
Reversible Markov Chains / 19.2：
Finite Electrical Networks / 19.3：
Recurrence and Transience / 19.4：
Network Reduction / 19.5：
Random Walk in a Random Environment / 19.6：
Ergodic Theory / 20：
Ergodic Theorems / 20.1：
Examples / 20.3：
Application: Recurrence of Random Walks / 20.4：
Mixing / 20.5：
Brownian Motion / 21：
Continuous Versions / 21.1：
Construction and Path Properties / 21.2：
Strong Markov Property / 21.3：
Supplement: Feller Processes / 21.4：
Construction via L[superscript 2]-Approximation / 21.5：
The Space C([0, [infinity])) / 21.6：
Convergence of Probability Measures on C([0, [infinity])) / 21.7：
Donsker's Theorem / 21.8：
Pathwise Convergence of Branching Processes* / 21.9：
Square Variation and Local Martingales / 21.10：
Law of the Iterated Logarithm / 22：
Iterated Logarithm for the Brownian Motion / 22.1：
Skorohod's Embedding Theorem / 22.2：
Hartman-Wintner Theorem / 22.3：
Large Deviations / 23：
Cramer's Theorem / 23.1：
Large Deviations Principle / 23.2：
Sanov's Theorem / 23.3：
Varadhan's Lemma and Free Energy / 23.4：
The Poisson Point Process / 24：
Random Measures / 24.1：
Properties of the Poisson Point Process / 24.2：
The Poisson-Dirichlet Distribution* / 24.3：
The Ito Integral / 25：
Ito Integral with Respect to Brownian Motion / 25.1：
Ito Integral with Respect to Diffusions / 25.2：
The Ito Formula / 25.3：
Dirichlet Problem and Brownian Motion / 25.4：
Recurrence and Transience of Brownian Motion / 25.5：
Stochastic Differential Equations / 26：
Strong Solutions / 26.1：
Weak Solutions and the Martingale Problem / 26.2：
Weak Uniqueness via Duality / 26.3：
References
Notation Index
Name Index
Subject Index
Preface
Basic Measure Theory / 1：
Classes of Sets / 1.1：
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