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Malliavin differentiability of solutions of rough differential equations (1312.7621v3)
Published 30 Dec 2013 in math.PR
Abstract: In this paper we study rough differential equations driven by Gaussian rough paths from the viewpoint of Malliavin calculus. Under mild assumptions on coefficient vector fields and underlying Gaussian processes, we prove that solutions at a fixed time is smooth in the sense of Malliavin calculus. Examples of Gaussian processes include fractional Brownian motion with Hurst parameter larger than $1/4$.