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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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