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

Subject Matter

 * Probability Theory

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