Advertisement

© 1965

Markov Processes

Volume 1

Book

Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GL, volume 121/122)

Table of contents

About this book

Introduction

The modem theory of Markov processes has its origins in the studies of A. A. MARKOV (1906-1907) on sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian motion (L. BACHELlER 1900, A. EIN­ STEIN 1905). The first correct mathematical construction of a Markov process with continuous trajectories was given by N. WIENER in 1923. (This process is often called the Wiener process.) The general theory of Markov processes was developed in the 1930's and 1940's by A. N. KOL­ MOGOROV, W. FELLER, W. DOEBLlN, P. LEVY, J. L. DOOB, and others. During the past ten years the theory of Markov processes has entered a new period of intensive development. The methods of the theory of semigroups of linear operators made possible further progress in the classification of Markov processes by their infinitesimal characteristics. The broad classes of Markov processes with continuous trajectories be­ came the main object of study. The connections between Markov pro­ cesses and classical analysis were further developed. It has become possible not only to apply the results and methods of analysis to the problems of probability theory, but also to investigate analytic problems using probabilistic methods. Remarkable new connections between Markov processes and potential theory were revealed. The foundations of the theory were reviewed critically: the new concept of strong Markov process acquired for the whole theory of Markov processes great importance.

Keywords

Brownian motion Law of large numbers Markov Markov process Probability theory

Authors and affiliations

  1. 1.University of MoscowRussia

Bibliographic information

  • Book Title Markov Processes
  • Book Subtitle Volume 1
  • Authors Evgenij Borisovic Dynkin
  • Series Title Die Grundlehren der Mathematischen Wissenschaften
  • DOI https://doi.org/10.1007/978-3-662-00031-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1965
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-03301-1
  • Softcover ISBN 978-3-662-00033-5
  • eBook ISBN 978-3-662-00031-1
  • Series ISSN 0072-7830
  • Edition Number 1
  • Number of Pages XII, 366
  • Number of Illustrations 1 b/w illustrations, 0 illustrations in colour
  • Additional Information Title of the original Russian edition: Osnovy teorii Markovskich processov
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
Industry Sectors
Pharma
Biotechnology
IT & Software
Telecommunications
Finance, Business & Banking
Electronics
Energy, Utilities & Environment
Aerospace
Oil, Gas & Geosciences
Engineering