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Softcover ISBN:  9780821851494 
Product Code:  CONM/149 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9780821877401 
Product Code:  CONM/149.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821851494 
eBook ISBN:  9780821877401 
Product Code:  CONM/149.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 

Book DetailsContemporary MathematicsVolume: 149; 1993; 347 ppMSC: 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 ]