Random dynamical systems, rough paths and rough flows

By Ismaël F. Bailleul, M. Scheutzow. 2016

49 citations recorded by the source corpus.

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 [26] induce random dynamical systems.

Subfields: Control and Systems Engineering, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2d2c8077b5c6fe9eb331b9891d35b3abcad07183