Abstract
Let P2 be the space of probability measures on Rd having finite second moment, and consider the Riemannian structure on P2 induced by the intrinsic derivative on the L2-tangent space. By using stochastic analysis on the tangent space, we construct an Ornstein−Uhlenbeck (OU) type Dirichlet form on P2 whose generator is formally given by the intrinsic Laplacian with a drift. The log-Sobolev inequality holds and the associated Markov semigroup is L2-compact. Perturbations of the OU Dirichlet form are also studied.
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