Detailansicht
Dirichlet Forms and Analysis on Wiener Space
eBook - ISSN
ISBN/EAN: 9783110858389
Umbreit-Nr.: 8509617
Sprache:
Deutsch
Umfang: 335 S.
Format in cm:
Einband:
Keine Angabe
Erschienen am 13.10.2010
Auflage: 1/2010
E-Book
Format: PDF
DRM: Adobe DRM
- Zusatztext
- <p>The subject of this book is analysis on Wiener space by means of Dirichlet forms and Malliavin calculus. There are already several literature on this topic, but this book has some different viewpoints.</p><p>First the authors review the theory of Dirichlet forms, but they observe only functional analytic, potential theoretical and algebraic properties. They do not mention the relation with Markov processes or stochastic calculus as discussed in usual books (e.g. Fukushimas book). Even on analytic properties, instead of mentioning the Beuring-Deny formula, they discuss carré du champ operators introduced by Meyer and Bakry very carefully. Although they discuss when this carré du champ operator exists in general situation, the conditions they gave are rather hard to verify, and so they verify them in the case of Ornstein-Uhlenbeck operator in Wiener space later. (It should be noticed that one can easily show the existence of carré du champ operator in this case by using Shigekawas H-derivative.)</p><p>In the part on Malliavin calculus, the authors mainly discuss the absolute continuity of the probability law of Wiener functionals. The Dirichlet form corresponds to the first derivative only, and so it is not easy to consider higher order derivatives in this framework. This is the reason why they discuss only the first step of Malliavin calculus. On the other hand, they succeeded to deal with some delicate problems (the absolute continuity of the probability law of the solution to stochastic differential equations with Lipschitz continuous coefficients, the domain of stochastic integrals (Itô-Ramer-Skorokhod integrals), etc.).</p><p>This book focuses on the abstract structure of Dirichlet forms and Malliavin calculus rather than their applications. However, the authors give a lot of exercises and references and they may help the reader to study other topics which are not discussed in this book.</p><p>Zentralblatt Math, Reviewer: S.Kusuoka (Hongo)</p><p></p>
- Kurztext
- <p>The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist.</p> <p>The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level.</p> <p>The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. </p> <p>Please submit any book proposals to <a href="mailto:n.jacob@swansea.ac.uk">Niels Jacob</a>.</p>
- Autorenportrait
- <p><strong>Nicolas Bouleau</strong>, École Polytechnique, Paris, France;<strong>Francis Hirsch</strong>, Université d'Évry-Val d'Essonne, Évry, France.</p>