Geometry on the Wasserstein Space Over a Compact Riemannian Manifold

Ding, Hao; Fang, Shizan

doi:10.1007/s10473-021-0612-4

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2022

2024

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Cited by 2 publications

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“…The Ricci curvature was calculated in [24], while the Levi-Civita connection and parallel displacement have been studied in [10].…”

Section: Introductionmentioning

confidence: 99%

Ornstein-Uhlenbeck Type Processes on Wasserstein Space

Ren¹,

Wang²

2022

Preprint

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The Wasserstein space P 2 consists of square integrable probability measures on R d and is equipped with the intrinsic Riemannian structure. By using stochastic analysis on the tangent space, we construct the Ornstein-Uhlenbeck (O-U) process on P 2 whose generator is formulated as the intrinsic Laplacian with a drift. This process satisfies the log-Sobolev inequality and has L 2 -compact Markov semigroup. Due to the important role played by O-U process in Malliavin calculus on the Wiener space, this measure-valued process should be a fundamental model to develop stochastic analysis on the Wasserstein space. Perturbations of the O-U process is also studied.

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“…The Ricci curvature was calculated in [24], while the Levi-Civita connection and parallel displacement have been studied in [10].…”

Section: Introductionmentioning

confidence: 99%