Boundary Value Problems and Markov Processes

This volume is devoted to a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel' boundary conditions in probability theory.  Analytically, a Markovian particle in a do

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Kazuaki Taira

Boundary Value Problems and Markov Processes Second Edition

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Kazuaki Taira University of Tsukuba Institute of Mathematics Tsukuba Ibaraki 305-8571 Japan [email protected]

ISSN 0075-8434 e-ISSN 1617-9692 ISBN 978-3-642-01676-9 e-ISBN 978-3-642-01677-6 DOI 10.1007/978-3-642-01677-6 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009928104 Mathematics Subject Classification (2000): 35J25, 47D05, 47D07, 60J35, 35K60 c Springer-Verlag Berlin Heidelberg 2009  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. Violations are liable to prosecution under the German Copyright Law. 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. Cover design: SPi Publisher Services Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

To the memory of Professor Kiyosi Itˆ o (1915–2008)

Preface to the Second Edition

This monograph is an expanded and revised version of a set of lecture notes for the graduate courses given by the author both at Hiroshima University (1995– 1997) and at the University of Tsukuba (1998–2000) which were addressed to the advanced undergraduates and beginning-graduate students with interest in functional analysis, partial differential equations and probability. The first edition of this monograph, which was based on the lecture notes given at the University of Tsukuba (1988–1990), was published in 1991. This edition was found useful by a number of people, but it went out of print after a few years. This second edition has been revised to streamline some of the analysis and to give better coverage of important examples and applications. The errors in the first printing are corrected thanks to kind remarks of many friends. In order to make the monograph more up-to-date, additional references have been included in the bibliography. This second edition may be considered as a short introduction to the more advanced book “Semigroups, boundary value problems and Markov processes” which was published in the Springer Monographs in Mathematics series in 2004. For graduate students working in functional analysis, partial differential equations and probability, it may serve as an effective introduction to these three interrelated fields of analysis. For graduate students about to major in the subject and mathematicians in the field looking for a c