Fractal dimensions of rough differential equations driven by fractional Brownian motions

In this work we study fractal properties of a d-dimensional rough differential equation driven by fractional Brownian motions with Hurst parameter H>14. In particular, we show that the Hausdorff dimension of the sample paths of the solution is min{d,1H} and that the Hausdorff dimension of the level set Lx={t∈[ϵ,1]:Xt=x} is 1−dH with positive probability when dH<1.