Random dynamical systems, rough paths and rough flows

被引：31

作者：

Bailleul, I. ^{[1
]}

Riedel, S. ^{[2
,3
]}

Scheutzow, M. ^{[3
]}

机构：

[1] Inst Rech Math Rennes, Rennes, France

[2] Univ Cologne, Math Inst, Cologne, Germany

[3] Tech Univ Berlin, Inst Math, Berlin, Germany

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 262卷 / 12期

关键词：

DIFFERENTIAL-EQUATIONS DRIVEN; HYPOELLIPTIC SDES DRIVEN; BROWNIAN MOTIONS; WIENER-PROCESSES; ERGODICITY; ATTRACTORS; DIMENSION;

D O I：

10.1016/j.jde.2017.02.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We analyze common lifts of stochastic processes to rough paths/rough drivers-valued processes and give sufficient conditions for the cocycle property to hold for these lifts. We show that random rough differential equations driven by such lifts induce random dynamical systems. In particular, our results imply that rough differential equations driven by the lift of fractional Brownian motion in the sense of Friz-Victoir [26] induce random dynamical systems. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：5792 / 5823

页数：32

共 51 条

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