Markov Processes. Structure and Asymptotic Behavior

This book is concerned with a set of related problems in probability theory that are considered in the context of Markov processes. Some of these are natural to consider, especially for Markov processes. Other problems have a broader range of validity but

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H erausgegeben von

J. L. Doob . A. Grothendieck . E. Heinz' F. Hirzebruch E. Hopf· W. Maak . S. MacLane . W. Magnus· J. K. Moser M. M. Postnikov . F. K. Schmidt· D. S. Scott· K. Stein Geschaftsfohrende H erausgeber

B. Eckmann und B. L. van der Waerden

Murray Rosenblatt

Markov Processes. Structure and Asymptotic Behavior

Springer-Verlag Berlin Heidelberg New York 1971

Prof. Murray Rosenblatt University of California, San Diego, La Jolla, California

Geschiiftsfiihrende Herausgeber:

Prof. Dr. B. Eckmann Eidgenossische Technische Hochschule Ziirich

Prof. Dr. B. L. van der Waerden Mathematisches Institut der Universitat Ziirich

AMS Subject Classifications (1970) Primary 60J05, 60F05 Secondary 60B99, 60010, 60050, 60J10, 60J15, 60J20, 60025

ISBN -13 :978-3-642-65240-0 e- ISBN -13: 978-3-642-65238-7 DOl: 10.1007/978-3-642-65238-7 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under §54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by SpringerVerlag Berlin Heidelberg 1971. Library of Congress Catalog Card Number 70-161441. Softcover reprint of the hardcover 18t edition 1971.

Murray Rosenblatt

Markov Processes. Structure and Asymptotic Behavior

Springer-Verlag New York Heidelberg Berlin 1971

Prof. Murray Rosenblatt University of California, San Diego, La Jolla, California

Geschiiftsfiihrende Herausgeber:

Prof. Dr. B. Eckmann Eidgenossische Technische Hochschule Ziirich

Prof. Dr. B. L. van der Waerden Mathematisches Institut der Universitat Ziirich

AMS Subject Classifications (1970) Primary 60J05, 60F05 Secondary 60B99, 60010, 60050, 60J10, 60J15, 60J20, 60025

ISBN -13 :978-3-642-65240-0 e- ISBN -13: 978-3-642-65238-7 DOl: 10.1007/978-3-642-65238-7 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under §54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by SpringerVerlag Berlin Heidelberg 1971. Library of Congress Catalog Card Number 70-161441. Softcover reprint of the hardcover 18t edition 1971.

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Preface This book is concerned with a set of related problems in probability theory that are considered in the context of Markov processes. Some of these are natural to consider, especially for Markov processes. Other problems have a broader range of validity but are convenient to pose for Markov processes. The book can be used as the basis for an interesting co