Random dynamical systems, rough paths and rough flows
Probability
2016-12-07 v1
Abstract
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 induce random dynamical systems.
Cite
@article{arxiv.1612.01955,
title = {Random dynamical systems, rough paths and rough flows},
author = {Ismael Bailleul and Sebastian Riedel and Michael Scheutzow},
journal= {arXiv preprint arXiv:1612.01955},
year = {2016}
}
Comments
27 pages