Editorial Boar d Steven G. Krantz David Saltman (Chair) David Sattinger Ronald Stern 2000 Mathematics Subject Classification. Primary 60-01 Secondary 60G99. The author was supported in part by NSF Grant DMS-9876586 ABSTRACT. These lecture notes concentrate on some general facts and ideas of the theory of stochastic processes. The main objects of study are the Wiener processes, the stationary processes, the infinitely divisible processes, and the ltd stochastic equations. Although it is not possible to cover even a noticeable portion of the topics listed above in a short course, the author sincerely hopes that after having followed the material presented here the reader will have acquired a good understanding of what kind of results are available and what kind of techniques are used to obtain them. These notes are intended for graduate students and scientists in mathematics, physics and engineering interested in the theory of random processes and its applications. Library of Congress Cataloging-in-Publication Data Krylov, N. V. (Nikola! Vladimirovich) Introduction to the theory of random processes / N. V. Krylov p. cm. - (Graduate studies in mathematics, ISSN 1065-7339 v. 43) Includes bibliographical references and index. ISBN 0-8218-2985-8 (alk. paper) 1. Stochastic processes. I. Title. II. Series. QA274 .K79 2002 519.2/3-dc21 2002018241 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, P. O. Box 6248, Providence, Rhode Island 02940-6248. Requests can also be made by e-mail to reprint-permission@ams.org. © 2002 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. @ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at URL: http://www.ams.org/ 10 9 8 7 6 5 4 3 2 1 07 06 05 04 03 02
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