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Product Code:  CONM/149 
347 pp 
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Electronic ISBN:  9780821877401 
Product Code:  CONM/149.E 
347 pp 
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Book DetailsContemporary MathematicsVolume: 149; 1993MSC: Primary 60;
Wolfgang Doeblin, one of the greatest probabilists of this century, died in action during World War II at the age of twentyfive. 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.
ReadershipResearchers in probability and science historians.

Table of Contents

Deblin’s Life and Work [ MR 1229951 ]

Bernard Bru  Doeblin’s life and work from his correspondence [ MR 1229952 ]

Kai Lai Chung  Reminiscences of one of Doeblin’s papers [ MR 1229953 ]

Coupling [ MR 1229951 ]

Thomas M. Liggett  The coupling technique in interacting particle systems [ MR 1229954 ]

Hermann Thorisson  Coupling and shiftcoupling random sequences [ MR 1229955 ]

Continued Fractions and Ergodicity [ MR 1229951 ]

Marius Iosifescu  Doeblin and the metric theory of continued fractions: a functionaltheoretic solution to Gauss’ 1812 problem [ MR 1229956 ]

Marius Iosifescu  A basic tool in mathematical chaos theory: Doeblin and Fortet’s ergodic theorem and Ionescu Tulcea and Marinescu’s generalization [ MR 1229957 ]

Marius Iosifescu and Sofia Kalpazidou  The nearest integer continued fraction expansion: an approach in the spirit of Doeblin [ MR 1229958 ]

Independent and Weakly Dependent Random Variables [ MR 1229951 ]

M. Csörgő, L. Horváth, Q.M. Shao and B. Szyszkowicz  On the weighted asymptotics of partial sums and empirical processes of independent random variables [ MR 1229959 ]

Mikhail  Homoclinic approch to the central limit theorem for dynamical systems

Magda Peligrad  Asymptotic results for $\phi $mixing sequences [ MR 1229961 ]

Murray Rosenblatt  The central limit theorem and Markov sequences [ MR 1229962 ]

Homogeneous and Nonhomogeneous Markov Chains [ MR 1229951 ]

I. Fleischer and A. Joffe  Behaviour of infinite products with applications to nonhomogeneous Markov chains [ MR 1229963 ]

E. Seneta  Applications of ergodicity coefficients to homogeneous Markov chains [ MR 1229964 ]

Markov Processes [ MR 1229951 ]

I. Cuculescu  Applications of some constructions of Markov processes [ MR 1229965 ]

S. P. Meyn and R. L. Tweedie  The Doeblin decomposition [ MR 1229966 ]

S. P. Meyn and R. L. Tweedie  Generalized resolvents and Harris recurrence of Markov processes [ MR 1229967 ]

Stochastic and Nonstochastic Matrices [ MR 1229951 ]

Joel E. Cohen, Yves Derriennic and Gh. Zbăganu  Majorization, monotonicity of relative entropy, and stochastic matrices [ MR 1229968 ]

Harry Cohn  Products of stochastic, nonstochastic, and random matrices [ MR 1229969 ]

J. Hajnal  Shuffling with two matrices [ MR 1229970 ]

Stochastic Processes [ MR 1229951 ]

K. B. Athreya  Continuous time gambling problems [ MR 1229971 ]

Erwin Bolthausen  Stochastic processes with long range interactions of the paths [ MR 1229972 ]

Arunava Mukherjea  Some remarks on products of random affine maps on $({\bf R}^+)^d$ [ MR 1229973 ]

P. E. Nüesch  A multivariate look at E. Sparre Andersen’s equivalence principle [ MR 1229974 ]

Peter Ney and Esa Nummelin  Regeneration for chains of infinite order and random maps [ MR 1229975 ]


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Wolfgang Doeblin, one of the greatest probabilists of this century, died in action during World War II at the age of twentyfive. 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.
Researchers in probability and science historians.

Deblin’s Life and Work [ MR 1229951 ]

Bernard Bru  Doeblin’s life and work from his correspondence [ MR 1229952 ]

Kai Lai Chung  Reminiscences of one of Doeblin’s papers [ MR 1229953 ]

Coupling [ MR 1229951 ]

Thomas M. Liggett  The coupling technique in interacting particle systems [ MR 1229954 ]

Hermann Thorisson  Coupling and shiftcoupling random sequences [ MR 1229955 ]

Continued Fractions and Ergodicity [ MR 1229951 ]

Marius Iosifescu  Doeblin and the metric theory of continued fractions: a functionaltheoretic solution to Gauss’ 1812 problem [ MR 1229956 ]

Marius Iosifescu  A basic tool in mathematical chaos theory: Doeblin and Fortet’s ergodic theorem and Ionescu Tulcea and Marinescu’s generalization [ MR 1229957 ]

Marius Iosifescu and Sofia Kalpazidou  The nearest integer continued fraction expansion: an approach in the spirit of Doeblin [ MR 1229958 ]

Independent and Weakly Dependent Random Variables [ MR 1229951 ]

M. Csörgő, L. Horváth, Q.M. Shao and B. Szyszkowicz  On the weighted asymptotics of partial sums and empirical processes of independent random variables [ MR 1229959 ]

Mikhail  Homoclinic approch to the central limit theorem for dynamical systems

Magda Peligrad  Asymptotic results for $\phi $mixing sequences [ MR 1229961 ]

Murray Rosenblatt  The central limit theorem and Markov sequences [ MR 1229962 ]

Homogeneous and Nonhomogeneous Markov Chains [ MR 1229951 ]

I. Fleischer and A. Joffe  Behaviour of infinite products with applications to nonhomogeneous Markov chains [ MR 1229963 ]

E. Seneta  Applications of ergodicity coefficients to homogeneous Markov chains [ MR 1229964 ]

Markov Processes [ MR 1229951 ]

I. Cuculescu  Applications of some constructions of Markov processes [ MR 1229965 ]

S. P. Meyn and R. L. Tweedie  The Doeblin decomposition [ MR 1229966 ]

S. P. Meyn and R. L. Tweedie  Generalized resolvents and Harris recurrence of Markov processes [ MR 1229967 ]

Stochastic and Nonstochastic Matrices [ MR 1229951 ]

Joel E. Cohen, Yves Derriennic and Gh. Zbăganu  Majorization, monotonicity of relative entropy, and stochastic matrices [ MR 1229968 ]

Harry Cohn  Products of stochastic, nonstochastic, and random matrices [ MR 1229969 ]

J. Hajnal  Shuffling with two matrices [ MR 1229970 ]

Stochastic Processes [ MR 1229951 ]

K. B. Athreya  Continuous time gambling problems [ MR 1229971 ]

Erwin Bolthausen  Stochastic processes with long range interactions of the paths [ MR 1229972 ]

Arunava Mukherjea  Some remarks on products of random affine maps on $({\bf R}^+)^d$ [ MR 1229973 ]

P. E. Nüesch  A multivariate look at E. Sparre Andersen’s equivalence principle [ MR 1229974 ]

Peter Ney and Esa Nummelin  Regeneration for chains of infinite order and random maps [ MR 1229975 ]