Essentials of Stochastic Processes
This book is for a first course in stochastic processes taken by undergraduates or master’s students who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, a
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For further volumes: http://www.springer.com/series/417
Richard Durrett
Essentials of Stochastic Processes Second Edition
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Richard Durrett Duke University Department of Mathematics Box 90320 Durham North Carolina USA
ISSN 1431-875X ISBN 978-1-4614-3614-0 ISBN 978-1-4614-3615-7 (eBook) DOI 10.1007/978-1-4614-3615-7 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012937472 © Springer Science+Business Media, LLC 1999, 2012 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
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Preface
Between the first undergraduate course in probability and the first graduate course that uses measure theory, there are a number of courses that teach Stochastic Processes to students with many different interests and with varying degrees of mathematical sophistication. To allow readers (and instructors) to choose their own level of detail, many of the proofs begin with a nonrigorous answer to the question “Why is this true?” followed by a Proof that fills in the missing details. As it is possible to drive a car without knowing about the working of the internal combustion engine, it is also possible to apply the theory of Markov chai
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