AVERAGING DYNAMICS DRIVEN BY FRACTIONAL BROWNIAN MOTION

被引：57

作者：

Hairer, Martin ^{[1
]}

Li, Xue-Mei ^{[1
]}

机构：

[1] Imperial Coll London, London, England

来源：

ANNALS OF PROBABILITY | 2020年 / 48卷 / 04期

关键词：

Fractional Brownian motion; averaging; slow/fast system; sewing lemma; STOCHASTIC DIFFERENTIAL-EQUATIONS; EXISTENCE; ERGODICITY; INEQUALITY; UNIQUENESS; BOUNDS;

D O I：

10.1214/19-AOP1408

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：1826 / 1860

页数：35

共 35 条

[1]

[Anonymous], 1990, CAMBRIDGE STUD ADV M

[2] BOUNDS FOR FUNDAMENTAL SOLUTION OF A PARABOLIC EQUATION [J].