A Bismut-Elworthy inequality for a Wasserstein diffusion on the circle
Abstract
We introduce in this paper a strategy to prove gradient estimates for some infinite-dimensional diffusions on $L_2$-Wasserstein spaces. For a specific example of a diffusion on the $L_2$-Wasserstein space of the torus, we get a Bismut-Elworthy-Li formula up to a remainder term and deduce a gradient estimate with a rate of blow-up of order $\mathcal{O}(t^{-(2+\epsilon)})$.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2020
- DOI:
- 10.48550/arXiv.2005.04972
- arXiv:
- arXiv:2005.04972
- Bibcode:
- 2020arXiv200504972M
- Keywords:
-
- Mathematics - Probability