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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer Berlin Heidelberg

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DOI

10.1007/978-1-4613-4148-2_7

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1432-0916

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The SmoluchowskiKramers Limit of Stochastic Diffe

Authors: Scott Hottovy Austin McDaniel Giovanni Volpe Jan Wehr
Publish Date: 2014/11/27
Volume: 336, Issue: 3, Pages: 1259-1283
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Abstract

We study a class of systems of stochastic differential equations describing diffusive phenomena The SmoluchowskiKramers approximation is used to describe their dynamics in the small mass limit Our systems have arbitrary statedependent friction and noise coefficients We identify the limiting equation and in particular the additional drift term that appears in the limit is expressed in terms of the solution to a Lyapunov matrix equation The proof uses a theory of convergence of stochastic integrals developed by Kurtz and Protter The result is sufficiently general to include systems driven by both white and Ornstein–Uhlenbeck colored noises We discuss applications of the main theorem to several physical phenomena including the experimental study of Brownian motion in a diffusion gradient

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