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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). (French) Zbl 0605.60058
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.
Reviewer: M.Chaleyat-Maurel

MSC:
60H07 Stochastic calculus of variations and the Malliavin calculus
60J45 Probabilistic potential theory
31C25 Dirichlet forms
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