Probability Theory III Stochastic Calculus
Preface In the axioms of probability theory proposed by Kolmogorov the basic "probabilistic" object is the concept of a probability model or probability space. This is a triple (n, F, P), where n is the space of elementary events or outcomes, F is a a-alg
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Editor-in-Chief: R. V. Gamkrelidze
Springer-Verlag Berlin Heidelberg GmbH
Yu. V. Prokhorov A. N. Shiryaev
Probability Theory III Stochastic Calculus
Springer
Consulting Editors of the Series: A.A. Agrachev, A.A. Gonchar, E.F. Mishchenko, N.M. Ostianu, V.P. Sakharova, A.B. Zhishchenko
Title of the Russian edition: Itogi nauki i tekhniki, Sovremennye problemy matematiki, Fundamental'nye napravleniya, VoI. 45, Teoriya veroyatoastej - 3, Publisher VINITI, Moscow 1989
Mathematics Subject Classification (1991): 60Hxx, 60G40, 60G44, 60G48, 60F17, 60J60, 6OJ65 ISSN 0938-0396 ISBN 978-3-642-08122-4 ISBN 978-3-662-03640-2 (eBook) DOI 10.1007/978-3-662-03640-2 This work is subject to copyright. AII rights are reserved. whether the whole or part of the material is concemed. specifically the rights of translation. reprinting. reuse ofillustrations. 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 ofthe German Copyright Law of September 9. 1965. in its current version. and permission for use mustalways be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1998 Originally published by Springer-Verlag Berlin Heidelberg New York in 1998 Softcover reprint of the hardcover 1st edition 1998 Typesetting: Camera·ready copy produced from the translators' input files using a Springer TEX macro package. 41/3143 - 5432 I 0- Printed on acid-free paper SPIN 10020167
List of Editors, Authors and Translators Editor-in-Chief
RV. Gamkrelidze, Russian Academy of Sciences, Steklov Mathematical Institute, u1. Gubkina 8, 117966 Moscow; Institute for Scientific Information (VINITI), u1. Usievicha 20a, 125219 Moscow, Russia; e-mail: [email protected] Consulting Editors
Yu. V. Prokhorov, Steklov Mathematical Institute, u1. Gubkina 8, 117966 Moscow, Russia, e-mail: [email protected] A. N. Shiryaev, Steklov Mathematical Institute, u1. Gubkina 8, 117966 Moscow, Russia, e-mail: [email protected] Authors
S. V. Anulova, Institut problem upravleniya RAN, u1. Provsoyuznaya 65, 117342 Moscow, Russia N. V. Krylov, Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA, e-mail: [email protected] R Sh. Liptser, Institute for Problems of Transmission of Information of the Russian Academy of Sciences, u1. Ermolovoj 15, 101447 Moscow, Russia; Department of Electrical Engineering-Systems, Tel Aviv University, Ramat Aviv 69978, Israel, e-mail: [email protected] A. N. Shiryaev, Steklov Mathematical Institute, u1. Gubkina 8, 117966 Moscow, Russia, e-mail: [email protected] A. Yu. Veretennikov, Inst. ofInformation Transmission Sciences, Russian Academy of Sciences, 19 Bolshoy Karetnii, 101447 Moscow, Russia, e-mail: [email protected], [email protected] Translator
P. B. Slater, Community and Organization Research Institute, University of California, San
