Malliavin differentiability of solutions of rough differential equations

摘要

In this paper we study rough differential equations driven by Gaussian roughpaths from the viewpoint of Malliavin calculus. Under mild assumptions oncoefficient vector fields and underlying Gaussian processes, we prove thatsolutions at a fixed time is smooth in the sense of Malliavin calculus.Examples of Gaussian processes include fractional Brownian motion with Hurstparameter larger than $1/4$.