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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
7
votes
Accepted
About the metrizability of the space of Probability measures $\mathcal{P}(S)$
I'm not really sure what Villani wrote in his monograph, but it is true that one needs to prove that the weak topology is induced by a distance, as a priori it could be another topology with the same …
2
votes
Elliptic Regularity with Gibbs Measure Satisfying Bakry-Emery Condition
For the estimate of the Hessian you might use Bochner's formula: on such weighted $R^d$ for any smooth compactly supported function $u$ it holds
$$
\nabla^*\nabla\frac{|\nabla u|^2}2=|D^2u|^2+\langle\ …