AVERAGING DYNAMICS DRIVEN BY FRACTIONAL BROWNIAN MOTION

• 成果类型: Article
• 署名作者: Hairer, Martin; Li, Xue-Mei
• 署名单位: Imperial College London
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1408
• 发表日期: 2020
• 页码: 1826-1860
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; EXISTENCE; ergodicity; INEQUALITY; uniqueness; bounds

摘要

We consider slow/fast systems where the slow system is driven by fractional Brownian motion with Hurst parameter H > 1/2. We show that unlike in the case H = 1/2, convergence to the averaged solution takes place in probability and the limiting process solves the 'naively' averaged equation. Our proof strongly relies on the recently obtained stochastic sewing lemma.