Stochastic Calculus and Applications
Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electr
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Samuel N. Cohen Robert J. Elliott
Stochastic Calculus and Applications Second Edition
Probability and Its Applications Series Editors Sidney I. Resnick Davar Khoshnevisan Andreas E. Kyprianou
More information about this series at http://www.springer.com/series/4893
Samuel N. Cohen
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Robert J. Elliott
Stochastic Calculus and Applications Second Edition
Robert J. Elliott School of Mathematics University of Adelaide Adelaide, Australia
Samuel N. Cohen Mathematical Institute University of Oxford Oxford, UK
Haskayne School of Business University of Calgary Calgary, Canada
ISSN 2297-0371 Probability and Its Applications ISBN 978-1-4939-2866-8 DOI 10.1007/978-1-4939-2867-5
ISSN 2297-0398 (electronic) ISBN 978-1-4939-2867-5 (eBook)
Library of Congress Control Number: 2015060429 Mathematics Subject Classification (2010): 60-01, 49-01, 93E11, 93E20 Springer New York Heidelberg Dordrecht London © Springer Science+Business Media New York 1982, 2015 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Science+Business Media LLC New York is part of Springer Science+Business Media (www. springer.com)
To Juli and Ann
I returned, and saw vnder the Sunne, That the race is not to the swift, nor the battell to the strong, neither yet bread to the wise, nor yet riches to men of vnderstanding, nor yet fauour to men of skil; but time and chance happeneth to them all. — Ecclesiastes 9:11 (AV, 1611)
The Queue of Fortune from John Lydgate’s The Siege of Troy, mid-fifteenth century. Copyright of The University of Manchester.
Preface to the Second Edition (2015)
The theory of probability and stochastic calculus has grown significantly since the publication of the first edition of this book. The theory of stochastic integration and semimartingales, a relatively recent development at the time of the first edition, is now a standard and significant part of the working mathematician’s toolkit. Concepts such as Backward SDEs, which were unheard of in 1982 (
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