Semigroups, Boundary Value Problems and Markov Processes
A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems.
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Kazuaki Taira
Semigroups, Boundary Value Problems and Markov Processes Second Edition
Springer Monographs in Mathematics
For further volumes: http://www.springer.com/series/3733
Kazuaki Taira
Semigroups, Boundary Value Problems and Markov Processes
Second Edition
123
Kazuaki Taira Institute of Mathematics University of Tsukuba Tsukuba Ibaraki Japan
ISSN 1439-7382 ISSN 2196-9922 (electronic) Springer Monographs in Mathematics ISBN 978-3-662-43695-0 ISBN 978-3-662-43696-7 (eBook) DOI 10.1007/978-3-662-43696-7 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2014946082 Mathematics Subject Classification: 35J25, 47D07, 47D05, 60J35, 60J60 © Springer-Verlag Berlin Heidelberg 2004, 2014 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To my mother Yasue Taira (1918–) and to the memory of my father Yasunori Taira (1915–1990)
Preface to the Second Edition
In this monograph we study a general class of elliptic boundary value problems for second-order integro-differential operators in partial differential equations, and prove that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, we construct a general class of Markov processes in probability
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