Applications to Partial Differential Equations
We now use the preceding results to solve the following generalization of the Dirichlet problem stated in the introduction:
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Stochastic Differential Equations An Introduction with Applications
Springer-Verlag Berlin Heidelberg GmbH
8emt IZJksendal Department of Mathematics University of Oslo Blindern, Oslo 3, Norway
AMS Subject Classification (1980) 6OHxx, 60G40, 60J45, 6OJ60, 93E11, 93E20 ISBN 978-3-540-15292-7 DOI 10.1007/978-3-662-13050-6
ISBN 978-3-662-13050-6 (eBook)
Library of Congress Cataloging in Publication Data 0ksendal, B. K. (Bernt Karsten). 1945 - Stochastic differential equations. (Universitext) Bibliography: p. Includes index. 1. Stochastic differential equations. 1. Title. 0A274.23.047 1985 519.2 85-12646 This work is subiect to copyright. AII rights are reserved. whether the whole or part of the material is concerned. specifically those of translation. reprinting. re-use of iIIustrations. broadcastlng. reproduction by photocopying machine or similar means. and storage in data banks. Under ยง 54 of the German Copyright Law where copies are made for other than private use. a fee is payable to "Verwertungsgesellschaft Wort". Munich. C Springer-Verlag Berlin Heidelberg 1985 Originally published by Springer-Verlag Berlin Heidelberg New York Tokyo in 1985
2141/3140-543210
To my family
Eva, Elise, Anders, and Karina
Preface
These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presentation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applications outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly developing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and completeness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications. These notes reflect this point of view. Such an approach enables us to reach the highlights of the theory quicker and easier. Thus it is hoped that notes may contribute to fill a gap in the existing literature. The course is meant to be an appetizer~ If it succeeds in awaking further interest, the reader will have a large selection of excellen
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