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Pré-Publication, Document De Travail Année : 2023

Stochastic differential equations and stochastic parallel translations in the Wasserstein space

Résumé

We will develop some elements in stochastic analysis in the Wasserstein space $P_2(M)$ over a compact Riemannian manifold $M$, such as intrinsic It\^o formulae, stochastic regular curves and parallel translations along them. We will establish the existence of parallel translations along regular curves, or stochastic regular curves in case where $M$ is a torus. Surprisingly enough, in this last case, the equation defining stochastic parallel translations is a SDE on a Hilbert space, instead of a SPDE
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hal-04207784 , version 1 (14-09-2023)

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  • HAL Id : hal-04207784 , version 1

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Shizan Fang, Ding Hao, Li Xiang-Dong. Stochastic differential equations and stochastic parallel translations in the Wasserstein space. 2023. ⟨hal-04207784⟩
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