DIFFUSION APPROXIMATION FOR FULLY COUPLED STOCHASTIC DIFFERENTIAL EQUATIONS

• 成果类型: Article
• 署名作者: Roeckner, Michael; Xie, Longjie
• 署名单位: University of Bielefeld; Jiangsu Normal University; Jiangsu Normal University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1475
• 发表日期: 2021
• 页码: 1205-1236
• 关键词: averaging principle; poisson-equation; strong-convergence; large deviations; systems; homogenization; motion

摘要

We consider a Poisson equation in 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 multitime scales stochastic differential equations with only Holder 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.