A Variational Characterization of Langevin-Smoluchowski Diffusions

Ioannis Karatzas () and Bertram Tschiderer ()
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Ioannis Karatzas: Department of Mathematics, Columbia University, 2990 Broadway
Bertram Tschiderer: Faculty of Mathematics, University of Vienna

A chapter in Stochastic Analysis, Filtering, and Stochastic Optimization, 2022, pp 239-265 from Springer

Abstract: Abstract We show that Langevin–Smoluchowski 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 Langevin–Smoluchowski flow with respect to this Gibbs measure.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-98519-6_10

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DOI: 10.1007/978-3-030-98519-6_10

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