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.
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21 June 2022
The original version of the book was inadvertently published with incorrect abstracts in the chapters. This has now been amended.
In addition to this, the affiliation of author Dr. Bertram Tschiderer has been changed to Faculty of Mathematics, University of Vienna in the online version of Chapter 10.
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Karatzas, I., Tschiderer, B. (2022). A Variational Characterization of Langevin-Smoluchowski Diffusions. In: Yin, G., Zariphopoulou, T. (eds) Stochastic Analysis, Filtering, and Stochastic Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-98519-6_10
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DOI: https://doi.org/10.1007/978-3-030-98519-6_10
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-98518-9
Online ISBN: 978-3-030-98519-6
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