TY - JOUR
T1 - Ornstein−Uhlenbeck type processes on Wasserstein spaces
AU - Ren, Panpan
AU - Wang, Feng-Yu
PY - 2024/6
Y1 - 2024/6
N2 - 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. © 2024 Elsevier B.V.
AB - 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. © 2024 Elsevier B.V.
KW - Gaussian measure on Wasserstein space
KW - Ornstein–Uhlenbeck dirichlet form
KW - Tangent space
UR - http://www.scopus.com/inward/record.url?scp=85188174395&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85188174395&origin=recordpage
U2 - 10.1016/j.spa.2024.104339
DO - 10.1016/j.spa.2024.104339
M3 - RGC 21 - Publication in refereed journal
SN - 0304-4149
VL - 172
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
M1 - 104339
ER -