Wednesday, November 30, 2022 - 14:15 in V3-201 + Zoom
Ornstein-Uhlenbeck type processes on Wasserstein space
A talk in the Bielefeld Stochastic Afternoon series by
Panpan Ren
| Abstract: |
Let $P_2$ be the space of probability measures on $R^D$ having finite second moment, and consider the Riemannian structure on
$P_2$ induced by the intrinsic derivative on the $L_2$-tangent space. By using stochastic analysis on the tangent space, we construct the Ornstein-Uhlenbeck (O-U) process on $P_2$ whose generator is formally given by the intrinsic Laplacian with a drift. This process satisfies the Log-Sobolev inequality and has $L_2$-compact Markov semigroup. Given the importance of the O-U process in Malliavin calculus on the Wiener space, this measure-valued process might be a fundamental model to develop stochastic analysis on the Wasserstein space. Perturbations of the O-U process are also studied.
Within the CRC this talk is associated to the project(s): A5 |
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