SLOW-FAST SYSTEMS WITH FRACTIONAL ENVIRONMENT AND DYNAMICS

• 成果类型: Article
• 署名作者: Li, Xue-Mei; Sieber, Julian
• 署名单位: Imperial College London
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1779
• 发表日期: 2022
• 页码: 3964-4003
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; driven; CONVERGENCE; equilibrium

摘要

We prove a fractional averaging principle for interacting slow-fast systems. The mode of convergence is in Holder norm in probability. The main technical result is a quenched ergodic theorem on the conditioned fractional dynamics. We also establish geometric ergodicity for a class of fractional-driven stochastic differential equations, improving a recent result of Panloup and Richard.