Dirichlet Forms and Analysis on Wiener Space / / Francis Hirsch, Nicolas Bouleau.
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. First the authors review the theory of Dirichlet forms, but they observe only functional analytic,...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2010] ©1991 |
Year of Publication: | 2010 |
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Bouleau, Nicolas, author. aut http://id.loc.gov/vocabulary/relators/aut Dirichlet Forms and Analysis on Wiener Space / Francis Hirsch, Nicolas Bouleau. Reprint 2010 Berlin ; Boston : De Gruyter, [2010] ©1991 1 online resource (325 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Studies in Mathematics , 0179-0986 ; 14 Frontmatter -- I General Dirichlet forms -- II Dirichlet forms on vector spaces -- III Analysis on Wiener space -- IV Stochastic differential equations -- V The algebra of Dirichlet structures -- VI An extension of Girsanov’s theorem -- VII Quasi-everywhere convergence -- Notes -- Bibliography -- Index -- Backmatter restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. 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. Fukushima’s 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 Shigekawa’s H-derivative.) 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.). 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. Zentralblatt Math, Reviewer: S.Kusuoka (Hongo) Issued also in print. Mode of access: Internet via World Wide Web. In German. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Dirichlet forms. Malliavin calculus. Dirichletsche Form. Wiener-Raum. MATHEMATICS / General. bisacsh Hirsch, Francis, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package 9783110494938 ZDB-23-GSM Title is part of eBook package: De Gruyter DGBA Mathematics - 1990 - 1999 9783110637199 ZDB-23-GMA Title is part of eBook package: De Gruyter E-DITION: BEST OF MATHEMATICS 9783110233957 ZDB-23-DGQ print 9783110129199 https://doi.org/10.1515/9783110858389 https://www.degruyter.com/isbn/9783110858389 Cover https://www.degruyter.com/document/cover/isbn/9783110858389/original |
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German |
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author |
Bouleau, Nicolas, Bouleau, Nicolas, Hirsch, Francis, |
spellingShingle |
Bouleau, Nicolas, Bouleau, Nicolas, Hirsch, Francis, Dirichlet Forms and Analysis on Wiener Space / De Gruyter Studies in Mathematics , Frontmatter -- I General Dirichlet forms -- II Dirichlet forms on vector spaces -- III Analysis on Wiener space -- IV Stochastic differential equations -- V The algebra of Dirichlet structures -- VI An extension of Girsanov’s theorem -- VII Quasi-everywhere convergence -- Notes -- Bibliography -- Index -- Backmatter |
author_facet |
Bouleau, Nicolas, Bouleau, Nicolas, Hirsch, Francis, Hirsch, Francis, Hirsch, Francis, |
author_variant |
n b nb n b nb f h fh |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Hirsch, Francis, Hirsch, Francis, |
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f h fh |
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VerfasserIn VerfasserIn |
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Bouleau, Nicolas, |
title |
Dirichlet Forms and Analysis on Wiener Space / |
title_full |
Dirichlet Forms and Analysis on Wiener Space / Francis Hirsch, Nicolas Bouleau. |
title_fullStr |
Dirichlet Forms and Analysis on Wiener Space / Francis Hirsch, Nicolas Bouleau. |
title_full_unstemmed |
Dirichlet Forms and Analysis on Wiener Space / Francis Hirsch, Nicolas Bouleau. |
title_auth |
Dirichlet Forms and Analysis on Wiener Space / |
title_alt |
Frontmatter -- I General Dirichlet forms -- II Dirichlet forms on vector spaces -- III Analysis on Wiener space -- IV Stochastic differential equations -- V The algebra of Dirichlet structures -- VI An extension of Girsanov’s theorem -- VII Quasi-everywhere convergence -- Notes -- Bibliography -- Index -- Backmatter |
title_new |
Dirichlet Forms and Analysis on Wiener Space / |
title_sort |
dirichlet forms and analysis on wiener space / |
series |
De Gruyter Studies in Mathematics , |
series2 |
De Gruyter Studies in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2010 |
physical |
1 online resource (325 p.) Issued also in print. |
edition |
Reprint 2010 |
contents |
Frontmatter -- I General Dirichlet forms -- II Dirichlet forms on vector spaces -- III Analysis on Wiener space -- IV Stochastic differential equations -- V The algebra of Dirichlet structures -- VI An extension of Girsanov’s theorem -- VII Quasi-everywhere convergence -- Notes -- Bibliography -- Index -- Backmatter |
isbn |
9783110858389 9783110494938 9783110637199 9783110233957 9783110129199 |
issn |
0179-0986 ; |
url |
https://doi.org/10.1515/9783110858389 https://www.degruyter.com/isbn/9783110858389 https://www.degruyter.com/document/cover/isbn/9783110858389/original |
illustrated |
Not Illustrated |
doi_str_mv |
10.1515/9783110858389 |
oclc_num |
840444348 |
work_keys_str_mv |
AT bouleaunicolas dirichletformsandanalysisonwienerspace AT hirschfrancis dirichletformsandanalysisonwienerspace |
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ids_txt_mv |
(DE-B1597)55073 (OCoLC)840444348 |
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Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package Title is part of eBook package: De Gruyter DGBA Mathematics - 1990 - 1999 Title is part of eBook package: De Gruyter E-DITION: BEST OF MATHEMATICS |
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Dirichlet Forms and Analysis on Wiener Space / |
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Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package |
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