Formes de Dirichlet générales et densité des variables aléatoires réelles sur l'espace de Wiener. (General Dirichlet forms and density of real random variables on Wiener space)
type: Item
instance of: scholarly article
title: Formes de Dirichlet générales et densité des variables aléatoires réelles sur l'espace de Wiener. (General Dirichlet forms and density of real random variables on Wiener space)
zbMATH Open document ID: 0605.60058
DOI: 10.1016/0022-1236(86)90090-X
author: Nicolas Bouleau
author: Francis Hirsch
published in: Journal of Functional Analysis
publication date: 1986-01-01T00:00:00Z
review text: The authors extend the theory of Dirichlet forms as well as the properties of the operator ''carré du champ'' to measurable spaces without the topological assumption of local compactness. Under a hypothesis on the base measure, they develop a functional calculus and they prove the ''energy-image density property''. This general setting contains the case of the Ornstein-Uhlenbeck semi-group on Wiener space and it allows the authors to prove, in one dimension, that the law of the solution of a stochastic differential equation with Lipschitz coefficients has a density. This case was not handled by the classical stochastic calculus of variations.
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 31C25
zbMATH DE Number: 3978067
zbMATH Keywords: theory of Dirichlet forms
zbMATH Keywords: Ornstein-Uhlenbeck semi-group on Wiener space
zbMATH Keywords: classical stochastic calculus of variations
reviewed by: Mireille Chaleyat-Maurel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3978067