The Smoluchowski–Kramers limits of stochastic differential equations with irregular coefficients

Longjie Xie and Li Yang

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 91-115

Abstract: In this paper, we study the small mass limit of the dynamic of stochastic system with state dependent friction and diffusion. We prove the strong convergence of the original system under weak assumptions on the coefficients, where the limiting equation admits an additional noise-induced drift term. Furthermore, the rate of convergence is also obtained. Our results even provide non-trivial improvement of the previous limit theorems for the classical Langevin equation.

Keywords: Smoluchowski–Kramers approximation; Langevin equation; Noise-induced drift; Zvonkin’s transformation; Homogenization (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.04.016

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