Theory of Markov Processes

E. B. Dynkin, T. Köváry

• Publisher: Pergamon
• Year: 2014
• ISBN:
  9781483226101
• Topic: Mathematics
• Subtopic: Discrete Mathematics
• Index: Mathematics

Theory of Markov Processes provides information pertinent to the logical foundations of the theory of Markov random processes. This book discusses the properties of the trajectories of Markov processes and their infinitesimal operators. Organized into six chapters, this book begins with an overview of the necessary concepts and theorems from measure theory. This text then provides a general definition of Markov process and investigates the operations that make possible an inspection of the class of Markov processes corresponding to a given transition function. Other chapters consider the more complicated operation of generating a subprocess. This book discusses as well the construction of Markov processes with given transition functions. The final chapter deals with the conditions to be imposed on the transition function so that among the Markov processes corresponding to this function, there should be at least one. This book is a valuable resource for mathematicians, students, and research workers.

Table of contents

• Front Cover
• Theory of Markov Processes
• Copyright Page
• Table of Contents
• Preface
• Chapter 1. Introduction
• Chapter 2. Markov Processes
• Chapter 3. Subprocesses
• Chapter 4. The Construction of Markov Processes with Given Transition Functions
• Chapter 5. Strictly Markov Processes
• Chapter 6. Conditions for Boundedness and Continuity of a Markov Process
• Addendum - A Theorem Regarding the Prolongation of Capacities, and the Properties of Measurability of the Instants of First Departure
• Supplementary Notes
• References
• Alphabetical Index
• Index of Lemmas and Theorems
• Index of Notation