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XX: 12, 131-161, LNM 1204 (1986)
BOULEAU, Nicolas; HIRSCH, Francis
Propriété d'absolue continuité dans les espaces de Dirichlet et applications aux équations différentielles stochastiques (Dirichlet forms, Malliavin's calculus)
This is the main result of the ``Bouleau-Hirsch approach'' to absolute continuity in Malliavin calculus (see The Malliavin calculus and related topics by D. Nualart, Springer1995). In the framework of Dirichlet spaces, a general criterion for absolute continuity of random vectors is established; it involves the image of the energy measure. This leads to a Lipschitzian functional calculus for the Ornstein-Uhlenbeck Dirichlet form on Wiener space, and gives absolute continuity of the laws of the solutions to some SDE's with coefficients that can be uniformly degenerate
Comment: These results are extended by the same authors in their book Dirichlet Forms and Analysis on Wiener Space, De Gruyter 1991
Keywords: Dirichlet forms, Carré du champ, Absolute continuity of laws
Nature: Original
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