Grundlehren der mathematischen Wissenschaften

Markov Processes

Volume 1

Authors: Dynkin, Evgenij Borisovic

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About this book

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.

Table of contents (12 chapters)

  • Introduction

    Dynkin, E. B.

    Pages 1-19

  • Contraction semigroups of linear operators on Banach spaces

    Dynkin, E. B.

    Pages 19-46

  • Infinitesimal operators of transition functions

    Dynkin, E. B.

    Pages 47-77

  • Markov processes

    Dynkin, E. B.

    Pages 77-104

  • First entrance and exit times and the intrinsic topology in the state space

    Dynkin, E. B.

    Pages 104-131

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-662-00031-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-3-662-00033-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Markov Processes
Book Subtitle
Volume 1
Authors
Translated by
Fabius, J., Maitra, A., Majone, G., Greenberg, V.
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
121/122
Copyright
1965
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-00031-1
DOI
10.1007/978-3-662-00031-1
Softcover ISBN
978-3-662-00033-5
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XII, 366
Number of Illustrations and Tables
1 b/w illustrations
Additional Information
Title of the original Russian edition: Osnovy teorii Markovskich processov
Topics