# Book:E.B. Dynkin/Theory of Markov Processes

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## E.B. Dynkin:

## E.B. Dynkin: *Theory of Markov Processes*

Published $\text {1961}$, **Dover Publications**

- ISBN 0-486-45305-7 (translated by D.E. Brown).

### Subject Matter

### Contents

- Preface

- Chapter 1 - Introduction

- 1. Measurable spaces and measurable sets
- 2. Measures and integrals
- 3. Conditional probabilities and mathematical expectations
- 4. Topological measurable spaces
- 5. The construction of probability measures

- Chapter 2 - Markov Processes

- 1. The definition of Markov process
- 2. Stationary Markov processes
- 3. Equivalent Markov processes

- Chapter 3 - Subprocesses

- 1. The definition of subprocess. The connexion between subprocesses and multiplicative functionals
- 2. Subprocesses corresponding to admissible subsets. The generation of a part of a process
- 3. Subprocesses corresponding to admissible systems of subsets
- 4. The integral type of multiplicative functionals and the corresponding subprocesses
- 5. Stationary subprocesses of stationary Markov processes

- Chapter 4 - The Construction of Markov Processes with Given Transition Functions

- 1. Definition of transition function. Examples
- 2. The construction of Markov processes with given transition function
- 3. Stationary transition functions and the corresponding stationary Markov processes

- Chapter 5 - Strictly Markov Processes

- 1. Random variables independent of the future and s-past
- 2. Definition of strictly Markov process
- 3. Stationary strictly Markov process
- 4. Weakening the form of the condition for processes continuous from the right to be strictly Markov
- 5. Strictly Markov subprocesses
- 6. Criteria for a process to be strictly Markov

- Chapter 6 - Conditions for Boundedness and Continuity of a Markov Process

- 1. Introduction
- 2. Conditions for boundedness
- 3. Conditions for continuity from the right and absence of discontinuities of the second kind
- 4. Jump-type and step processes
- 5. Continuity conditions
- 6. A continuity theorem for strictly Markov processes
- 7. Examples

- Addendum - A Theorem Regarding the Prolongation of Capacities, and the Properties of Measurability of the Instants of First Departure

- 1. A theorem regarding the extension of capacities
- 2. Measurability theorems for the instants of first departure

- Supplementary Notes

- References

- Alphabetical Index

- Index of Lemmas and Theorems

- Index of Notation