**Contemporary Mathematics**

Volume: 149;
1993;
347 pp;
Softcover

MSC: Primary 60;

Print ISBN: 978-0-8218-5149-4

Product Code: CONM/149

List Price: $63.00

Individual Member Price: $50.40

**Electronic ISBN: 978-0-8218-7740-1
Product Code: CONM/149.E**

List Price: $63.00

Individual Member Price: $50.40

# Doeblin and Modern Probability

Share this page *Edited by *
*Harry Cohn*

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.

#### Table of Contents

# Table of Contents

## Doeblin and Modern Probability

- Contents v6 free
- Preface vii8 free
- Introduction ix10 free
- Doeblin's Life and Work 114 free
- Coupling 7386
- Continued Fractions and Ergodicity 97110
- Doeblin and the metric theory of continued fractions: A functional theoretic solution to Gauss' 1812 problem 97110
- A basic tool in mathematical chaos theory: Doeblin and Fortet's ergodic theorem and Ionescu Tulcea and Marinescu's generalization 111124
- The nearest integer continued fraction expansion: An approach in the spirit of Doeblin 125138

- Independent and Weakly Dependent Random Variables 139152
- Homogeneous and Non-homogeneous Markov Chains 179192
- Markov Processes 201214
- Stochastic and Nonstochastic Matrices 251264
- Stochastic Processes 289302
- Continuous time gambling problems 289302
- Stochastic processes with long range interactions of the paths 297310
- Some remarks on products of random affine maps on (R+)d 321334
- A multivariate look at E. Sparre Andersen's equivalence principle 331344
- Regeneration for chains of infinite order and random maps 339352

#### Readership

Researchers in probability and science historians.