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The Small-Mass Limit for Langevin Dynamics with Unbounded Coefficients and Positive Friction

Journal article
Authors David P. Herzog
Scott Hottovy
Giovanni Volpe
Published in Journal of Statistical Physics
Volume 163
Pages 659-673
ISSN 00224715
Publication year 2016
Published at
Pages 659-673
Language en
Keywords Locally Lipschitz coefficients, Small-mass limit, Smoluchowski–Kramers approximation
Subject categories Physical Sciences, Mathematics

Abstract

© 2016, Springer Science+Business Media New York. A class of Langevin stochastic differential equations is shown to converge in the small-mass limit under very weak assumptions on the coefficients defining the equation. The convergence result is applied to three physically realizable examples where the coefficients defining the Langevin equation for these examples grow unboundedly either at a boundary, such as a wall, and/or at the point at infinity. This unboundedness violates the assumptions of previous limit theorems in the literature. The main result of this paper proves convergence for such examples.

Page Manager: Webmaster|Last update: 9/11/2012
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