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 lawsNature: Original
Retrieve article from Numdam
XLIV: 04, 75-103, LNM 2046 (2012)
QIAN, Zhongmin;
YING, Jiangang
Martingale representations for diffusion processes and backward stochastic differential equations (
Stochastic calculus)
Keywords: Backward Stochastic Differential equations,
Dirichlet forms,
Hunt processes,
Martingales,
Natural filtration,
Non-linear equationsNature: Original
