Regularity of invariant measures : the case of non - constantdi usion
نویسندگان
چکیده
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 00) + B ru. Here A is a Lipschitz continuous, uniformly elliptic matrix-valued map and B is merely-square integrable. We also treat a class of corresponding innnite dimensional cases where IR d is replaced by a locally convex topological vector space X. In this cases is 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 ID 2;1 .
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