A variational characterization of Langevin$\boldsymbol{-}$Smoluchowski diffusions
Probability
2020-11-10 v2
Abstract
We show that LangevinSmoluchowski measure on path space is invariant under time-reversal, followed by stochastic control of the drift with a novel entropic-type criterion. Repeated application of these forward-backward steps leads to a sequence of stochastic control problems, whose initial/terminal distributions converge to the Gibbs probability measure of the diffusion, and whose values decrease to zero along the relative entropy of the LangevinSmoluchowski flow with respect to this Gibbs measure.
Cite
@article{arxiv.2010.04847,
title = {A variational characterization of Langevin$\boldsymbol{-}$Smoluchowski diffusions},
author = {Ioannis Karatzas and Bertram Tschiderer},
journal= {arXiv preprint arXiv:2010.04847},
year = {2020}
}