Poisson Point Processes and Their Application to Markov Processes
An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a gen
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Kiyosi Itô
Poisson Point Processes and Their Application to Markov Processes
SpringerBriefs in Probability and Mathematical Statistics Editor-in-chief Mark Podolskij, Aarhus C, Denmark Series editors Nina Gantert, Münster, Germany Richard Nickl, Cambridge, UK Sandrine Péché, Paris, France Gesine Reinert, Oxford, UK Mathieu Rosenbaum, Paris, France Wei Biao Wu, Chicago, USA
More information about this series at http://www.springer.com/series/14353
Kiyosi Itô
Poisson Point Processes and Their Application to Markov Processes Foreword by Shinzo Watanabe and Ichiro Shigekawa
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Kiyosi Itô (1915–2008) Kyoto University Kyoto Japan
Compiling Editors Shinzo Watanabe Kyoto University Kyoto Japan Ichiro Shigekawa Kyoto University Kyoto Japan
ISSN 2365-4333 ISSN 2365-4341 (electronic) SpringerBriefs in Probability and Mathematical Statistics ISBN 978-981-10-0271-7 ISBN 978-981-10-0272-4 (eBook) DOI 10.1007/978-981-10-0272-4 Library of Congress Control Number: 2015959578 © The Author(s) 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 This Springer imprint is published by SpringerNature The registered company is Springer Science+Business Media Singapore Pte Ltd.
Foreword
Professor Kiyosi Itô had been leaving Japan and working regularly in foreign countries for several years including 1969. During the summer vacation of that year, he returned to Japan, to his home in Kyoto, and had a pleasant time meeting again and communicating with Japanese researchers and students. He gave then a series of lectures at Kyoto University and Osaka University. The present volume consists of original manuscripts of those lectures. In the lectures, he treated a general theory of Poisson point processes and its applications to an extension problem (often called a boundary problem) of Markov processes. We know well that Itô applied the notion of Poisson point process to describe the sample functions of Lévy processes (additive processes, differential processes, or p
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