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+varepsilon )}).
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