Diffusion approximation for fully coupled stochastic differential equations

2020/08/11 by Michael Röckner, Röckner, Michael, Longjie Xie +1 · 5 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #35B30 #60H10 #60J60 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2008.04817

openalex publication_date 2020/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We consider a Poisson equation in \mathbb R^d for the elliptic operator corresponding to an ergodic diffusion process. Optimal regularity and smoothness with respect to the parameter are obtained under mild conditions on the coefficients. The result is then applied to establish a general diffusion approximation for fully coupled multi-time-scales stochastic differential equations with only Hölder continuous coefficients. Four different averaged equations as well as rates of convergence are obtained. Moreover, the convergence is shown to rely only on the regularities of the coefficients with respect to the slow variable, and does not depend on their regularities with respect to the fast component.

Citations

• Strong and weak convergence in the averaging principle for SDEs with Hölder coefficients

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