Markov Chains With Stationary Transition Probabilities
- PDF / 24,471,305 Bytes
- 312 Pages / 439.37 x 666.142 pts Page_size
- 101 Downloads / 265 Views
Series editors M. Berger P. de la Harpe F. Hirzebruch N.J. Hitchin L. Hörmander A. Kupiainen G. Lebeau F.-H. Lin B.C. Ngô M. Ratner D. Serre Ya.G. Sinai N.J.A. Sloane A.M. Vershik M. Waldschmidt Editor-in-Chief A. Chenciner J. Coates S.R.S. Varadhan
104
For further volumes: http://www.springer.com/series/138
Kai Lai Chung
Markov Chains With Stationary Transition Probabilities
Second Edition
Kai Lai Chung (1917-2009) Stanford University, USA
ISSN 0072-7830 ISBN-13: 978-3-642-62017-1 e-ISBN-13: 978-3-642-62015-7 DOl: 10.1007/978-3-642-62015-7 Springer Heidelberg Dordrecht London New York Library of Congress Catalog Card Number: 66-25793 Mathematics Subject Classification (2010): 60-XX, 60110
© by Springer-Verlag OHG, Berlin' Gottingen . © by Springer-Verlag, Berlin' Heidelberg 1967
Heidelberg 1960
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: VTEX, Vilnius
Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To my parents
Preface to the First Edition The theory of Markov chains, although a special case of Markov processes, is here developed for its own sake and presented on its own merits. In general, the hypothesis of a denumerable state space, which is the defining hypothesis of what we call a "chain" here, generates more clear-cut questions and demands more precise and definitive answers. For example, the principal limit theorem (§§ I.6, II.10), still the object of research for general Markov processes, is here in its neat final form; and the strong Markov property (§ II.9) is here always applicable. While probability theory has advanced far enough that a degree of sophistication is needed even in the limited context of this book, it is still possible here to keep the proportion of definitions to theorems relatively low. From the standpoint of the general theory of stochastic processes, a continuous parameter Markov chain appears to be the first essentially discontinuous process that has been studied in some detail. It is common that the sample functions of such a chain have discontinuities worse than jumps, and these baser discontinuities playa central role in the theory, of which the mystery remains to be completely unraveled. In this connection
