Book:E.B. Dynkin/Theory of Markov Processes
Jump to navigation
Jump to search
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