Semigroups, Boundary Value Problems and Markov Processes
The purpose of this book is to provide a careful and accessible account along modern lines of the subject wh ich the title deals, as weIl as to discuss prob lems of current interest in the field. Unlike many other books on Markov processes, this book foc
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Springer-Verlag Berlin Heidelberg GmbH
Kazuaki Taira
Semigroups, Boundary Value Problems and Markov Processes
,
Springer
Kazuaki Taira University ofTsukuba Institute of Mathematics 305-8571 Tsukuba, Ibaraki Japan e-mail: [email protected]
Cataloging-in-Publication Data applied for A catalog record for this book is avaiIable from the Library of Congress. Bibliographie information pubJished by Die Deutsche Bibliothek Die Deutsche Bibliothek Jist. this pubIication in the Deutsche Nationalbibliografie; detailed bibliographie data is avaiJable in the Internet at http://dnb.ddb.de
Mathematics Subject Classification (2000): 60J, 47D, 35J, 35B
ISBN 978-3-642-07371-7 ISBN 978-3-662-09857-8 (eBook) DOI 10.1007/978-3-662-09857-8
This work is subject to copyright. All rigbts 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 Berlin Heidelberg GmbH. Violations are Iiable for prosecution under the German Copyright Law.
http://www.springer.de CI Springer-Verlag Berlin Heidelberg 2004 Origina1Jy publisbed by Springer-Verlag Berlin Heidelberg New YOIk in 2004 Softcover reprint ofthe hardcover Ist edition 2004 The use of general descriptive names, registered names, trademarks, 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. Typesetting by the author using aSpringer T)lX macro package Cover production: Brich Kirchner, Heidelberg Printed on acid-free paper
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To my mother Yasue Taira and to the memory of my father Yasunori Taira
Preface
The purpose of this book is to provide a careful and accessible account along modern lines of the subject wh ich the title deals, as weIl as to discuss problems of current interest in the field. Unlike many other books on Markov processes, this book focuses on the relationship between Markov processes and elliptic boundary value problems, with emphasis on the study of analytic semigroups. More precisely, this book is devoted to the functional analytic approach to a class of degenerate boundary value problems for second-order elliptic integro-differential operators, called Waldenfels operators, whi:h includes as particular cases the Dirichlet and Robin problems. We prove that this class of boundary value problems provides a new example of analytic semigroups both in the LP topology and in the topology of uniform convergence. As an application, we construct a strong Markov process corresponding to such a physical phenomenon that a Markovian particle moves both by jumps and continuously in the s
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