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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. 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
3.

図書
図書
3. 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：
4.

図書
図書
4. 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：
5.

図書
図書
5. 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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6.

図書
図書
6. 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：
7.

図書
図書
7. 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
8.

図書
図書
8. 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：
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