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Ornstein−Uhlenbeck type processes on Wasserstein spaces

Author

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  • Ren, Panpan
  • Wang, Feng-Yu

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.

Suggested Citation

  • Ren, Panpan & Wang, Feng-Yu, 2024. "Ornstein−Uhlenbeck type processes on Wasserstein spaces," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:spapps:v:172:y:2024:i:c:s0304414924000450
    DOI: 10.1016/j.spa.2024.104339
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