Stochastic Partial Differential Equations A Modeling, White Noise Fu
The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs driven by space-time Brownian motion noise. In this, the second edition, the authors extend the theory
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Helge Holden Bernt Øksendal Jan Ubøe Tusheng Zhang
Stochastic Partial Differential Equations A Modeling, White Noise Functional Approach Second Edition
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Helge Holden Department of Mathematical Sciences Norwegian University of Science and Technology 7491 Trondheim Norway
Bernt Øksendal Department of Mathematics University of Oslo 0316 Oslo Blindern Norway [email protected]
and Center of Mathematics and Applications University of Oslo 0316 Oslo Norway [email protected] Jan Ubøe Department of Economics Norwegian School of Economics and Business Administration 5045 Bergen Norway [email protected]
Tusheng Zhang University of Manchester School of Mathematics Manchester M13 9PL United Kingdom [email protected]
Editorial Board: Sheldon Axler, San Francisco State University Vincenzo Capasso, Universit´a degli Studi di Milano Carles Casacuberta, Universitat de Barcelona Angus MacIntyre, Queen Mary, University of London Kenneth Ribet, University of California, Berkeley ´ Claude Sabbah, CNRS, Ecole Polytechnique Endre S¨uli, University of Oxford Wojbor Woyczy´nski, Case Western Reserve University ISBN 978-0-387-89487-4 e-ISBN 978-0-387-89488-1 DOI 10.1007/978-0-387-89488-1 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009938826 Mathematics Subject Classification (2000): 60H15, 35R60, 60H40, 60J60, 60J75 c First Edition published by Birkh¨auser Boston, 1996 c Second Edition published by Springer Science+Business Media, LLC, 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Eva, Qinghua, and Tatiana
At vide hvad man ikke v´ed, er dog en slags alvidenhed.
Knowing what thou knowest not is in a sense omniscience. Piet Hein
c Piet Hein gruk and grooks reprinted with kind permission of Piet Hein a.s., DK-Middelfart .
Preface to the Second Edition
Since the first edition of this book appeared in 1996, white noise theory and its applications have expanded to several areas. Important examples are (i) White noise theory for fractional Brownian motion. See, e.g., Biagini et al. (2008) and the references therein. (ii) White noise theory as a tool for Hida–Malliavin calculus and anticipative stochastic calculus, with a
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