Regularity of Invariant Measures: The Case of Non-constant Diffusion Part

✍ Scribed by V.I. Bogachev; N. Krylov; M. Röckner

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 896 KB
• Volume: 138
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1996.0063

✦ Synopsis

We prove regularity (i.e., smoothness) of measures + on R d satisfying the equation L*+=0 where L is an operator of type Lu=tr(Au")+B } {u. Here A is a Lipschitz continuous, uniformly elliptic matrix-valued map and B is merely +-square integrable. We also treat a class of corresponding infinite dimensional cases where R d is replaced by a locally convex topological vector space X. In this cases + is proved to be absolutely continuous w.r.t. a Gaussian measure on X and the square root of the Radon Nikodym density belongs to the Malliavin test function space D 2, 1 .