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
XXVII: 26, 302-303, LNM 1557 (1993)
HIRSCH, Francis
Représentation du processus d'Ornstein-Uhlenbeck à $n$ paramètres Retrieve article from Numdam
XLIII: 21, 451-503, LNM 2006 (2011)
HIRSCH, Francis;
PROFETA, Christophe;
ROYNETTE, Bernard;
YOR, Marc
Constructing self-similar martingales via two Skorokhod embeddings (
Martingale theory)
Keywords: Skorokhod embeddings,
Hardy-Littlewood functions,
Convex order,
Schauder fixed point theorem,
Self-similar martingales,
Karamata's representation theoremNature: Original
XLVII: 01, xi-xxxi, LNM 2137 (2015)
AZÉMA, Jacques;
BARRIEU, Pauline;
BERTOIN, Jean;
CABALLERO, Maria Emilia;
DONATI-MARTIN, Catherine;
ÉMERY, Michel;
HIRSCH, Francis;
HU, Yueyun;
LEDOUX, Michel;
NAJNUDEL, Joseph;
MANSUY, Roger;
MICLO, Laurent;
SHI, Zhan;
WILLIAMS, David
TémoignagesNature: Tribute
