Doeblin and modern probability : proceedings of the Doeblin Conference "50 Years after Doeblin: development in the theory of Markov chains, Markov processes, and sums of random variables" held November 2-7, 1991, with support from the Applied Probability Trust
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書誌事項
Doeblin and modern probability : proceedings of the Doeblin Conference "50 Years after Doeblin: development in the theory of Markov chains, Markov processes, and sums of random variables" held November 2-7, 1991, with support from the Applied Probability Trust
（Contemporary mathematics, v. 149）
American Mathematical Society, c1993
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注記
"Proceedings of the Doeblin Conference ... held November 2-7, 1991 at the University of Tubingen's Heinrich Fabri Institut, Blaubeuren, Germany, through the efforts of Professors H. Hering and J. Gani"--T.p. verso
Includes bibliographical references
内容説明・目次
内容説明
Wolfgang Doeblin, one of the greatest probabilists of this century, died in action during World War II at the age of twenty-five. He left behind several seminal contributions which have profoundly influenced the field and continue to provide inspiration for current research. This book is based on papers presented at the conference, 'Fifty Years after Doeblin: Developments in the Theory of Markov Chains, Markov Processes, and Sums of Random Variables', held at Blaubeuren, Germany, in November 1991. Presented here for the first time is an account of Doeblin's life and work, revealing the circumstances of his tragic death in 1940. Organized into sections according to topic, the papers describe both Doeblin's original contributions as well as current developments. With contributions by top probabilists from sixteen countries, this book will interest both researchers in probability and science historians.
目次
Doeblin's Life and Work Doeblin's life and work from his correspondence by B. Bru Reminiscences of one of Doeblin's papers by K. L. Chung Coupling The coupling technique in interacting particle systems by T. M. Liggett Coupling and shift-coupling random sequences by H. Thorisson Continued Fractions and Ergodicity Doeblin and the metric theory of continued fractions: A functional theoretic solution to Gauss' 1812 problem by M. Iosifescu A basic tool in mathematical chaos theory: Doeblin and Fortet's ergodic theorem and Ionescu Tulcea and Marinescu's generalization by M. Iosifescu The nearest integer continued fraction expansion: An approach in the spirit of Doeblin by M. Iosifescu and S. Kalpazidou Independent and Weakly Dependent Random Variables On the weighted asymptotics of partial sums and empirical processes of independent random variables by M. Csorgo, L. Horvath, Q.-M. Shao, and B. Szyszkowicz Homoclinic approach to the central limit theorem for dynamical systems by M. Gordin Asymptotic results for $\varphi$-mixing sequences by M. Peligrad The central limit theorem and Markov sequences by M. Rosenblatt Homogeneous and Non-homogeneous Markov Chains Behaviour of infinite products with applications to non-homogeneous Markov chains by I. Fleischer and A. Joffe Applications of ergodicity coefficients to homogeneous Markov chains by E. Seneta Markov Processes Applications of some constructions of Markov processes by I. Cuculescu The Doeblin decomposition by S. P. Meyn and R. L. Tweedie Generalized resolvents and Harris recurrence of Markov processes by S. P. Meyn and R. L. Tweedie Stochastic and Nonstochastic Matrices Majorization, monotonicity of relative entropy, and stochastic matrices by J. E. Cohen, Y. Derriennic, and Gh. Zbaganu Products of stochastic, nonstochastic, and random matrices by H. Cohn Shuffling with two matrices by J. Hajnal Stochastic Processes Continuous time gambling problems by K. B. Athreya Stochastic processes with long range interactions of the paths by E. Bolthausen Some remarks on products of random affine maps on $(R^+)^d$ by A. Mukherjea A multivariate look at E. Sparre Andersen's equivalence principle by P. E. Nuesch Regeneration for chains of infinite order and random maps by P. Ney and E. Nummelin.
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