probability theory

Smoluchowski-Kramers Approximation for Stochastic Differential Equations driven by Fractional Brownian Motion

arXiv:2607.11076

summary

The paper analyzes the Smoluchowski‑Kramers small‑mass limit for stochastic differential equations driven by fractional Brownian motion, establishing convergence rates and studying large and moderate deviation principles via weak convergence methods.

Abstract

In this paper, we discuss the validity of an approximation inspired by the Smoluchowski-Kramers approximation for a class of stochastic differential equations driven by fractional Brownian motion with additive noise. By rewriting such equations in the form of slow-fast systems and decomposing the fast component into three parts, we investigate the small mass limit of these equations and derive the corresponding convergence rates. Furthermore, under certain regularity conditions, we study the large and moderate deviation principles for a class of stochastic differential equations driven by fractional Brownian motion with small multiplicative noise via the weak convergence approach.

Topics & keywords

#smoluchowski-kramers approximation#fractional brownian motion#stochastic differential equations#small mass limit#large deviations#moderate deviationsadditive noisemultiplicative noiseslow-fast systemsweak convergence approachconvergence rates
Smoluchowski-Kramers Approximation for Stochastic Differential Equations driven by Fractional Brownian Motion · wovepaper