Markov Processes
Let us consider a particle moving in a space 5, called the state space. We assume the Markovian character of the motion that the particle that starts at x at present will move into B ⊂ S with probability p t (x,B) after time t irrespectively of its past m
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Springer-Verlag Berlin Heidelberg GmbH
Kiyosi Itö playinggo with Haruo Totoki (1934-1991) in 1969 at Itö's home at Aarhus (photo by S. A. Serensen)
Kiyosi Itö
Stochastic Processes Lectures given at Aarhus University
Edited by DIe E. Barndorff-Nielsen Ken-iti Sato
Springer
Kiyosi ItD Kyoto, Japan
Oie E. Barndorff-Nielsen Department of Mathematics University of Aarhus Ny Munkegade 8000 Aarhus, Denmark e-mail: [email protected]
Ken-iti Sato Hachiman-yama 1101-5-103 Tenpaku-ku, Japan e-mail: [email protected]
Cataloging-in-Publication Data applied for A catalog record for this book is available from the Library of Congress . Bibliographie information published by Die Deutsche Bibliothek Die Deut sche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographie data is available in the Internet at . Mathematics Subject Classification (2000): 60-02, 60E07, 60G51, 60J25 ISBN 978-3-642-05805-9 ISBN 978-3-662-10065-3 (eBook) DOI 10.I007/978-3-662-10065-3 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, 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 of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 2004
Originally published by Springer-Verlag Berlin Heidelberg New York in 2004. Softcover reprint of the hardcover Ist edition 2004 The use of general descriptive names, registered narnes, tradernarks, 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. Typeset by the editors. Cover design: design & production GmbH, Heidelberg 4t13142LK - 5 4 3 2 1 0 Printed on acid-free paper
Foreword
The volume Stochastic Processes by K. It ö was published as No. 16 of Lecture Notes Series from Mathemati cs Inst itute, Aarhus University in Augu st , 1969 , based on Lectures given at t hat Insti tute during t he acade mie year 19681969. The volume was as thick as 3.5 cm. , mimeogr aphed fro m ty pe writ ten manuscript and has been out of print for many years . Since it s a ppearance, it has served , for those abIe to obtain one of the relatively few copies available, as a highly readable introdu etion to basic part s of t he theories of addit ive pr ocesses (processes with indepe ndent increm ents) and of Markov processes. It contains, in par t icul ar, a clear and det ailed exposit ion of t he L évy-It ö decom position of add it ive pro cesses. E ncouraged by Professor It ó we have edited t he volume in t he present book form , amend ing t he text in a nu mb er of places an
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