论文标题
Wasserstein空间上的Ornstein-Uhlenbeck类型过程
Ornstein-Uhlenbeck Type Processes on Wasserstein Space
论文作者
论文摘要
令$ \ MATHCAL P_2 $为有限第二时$ \ r^d $的概率度量的空间，并考虑$ \ Mathcal P_2 $的Riemannian结构，由$ l^2 $ tangangengent Space上的固有导数引起。通过在切线空间上使用随机分析，我们在$ \ Mathcal P_2 $上构建了Ornstein $ - $ uhlenbeck（OU）型dirichlet形式，其发电机由固有的laplacian正式给出，并带有漂移。 log-sobolev不平等持有，关联的Markov Semigroup为$ l^2 $ - compact。 还研究了OU Dirichlet形式的扰动。
Let $\mathcal P_2$ be the space of probability measures on $\R^d$ having finite second moment, and consider the Riemannian structure on $\mathcal P_2$ induced by the intrinsic derivative on the $L^2$-tangent space. By using stochastic analysis on the tangent space, we construct an Ornstein$-$Uhlenbeck (OU) type Dirichlet form on $\mathcal P_2$ whose generator is formally given by the intrinsic Laplacian with a drift. The log-Sobolev inequality holds and the associated Markov semigroup is $L^2$-compact. Perturbations of the OU Dirichlet form are also studied.
