Fractal Dimensions of Rough Differential Equations Driven by Fractional Brownian Motions
Lou, Shuwen · Ouyang, Cheng
Original · EN
In this work we study fractal properties of rough differential equations driven by a fractional Brownian motions with Hurst parameter H>1/4. In particular, we show that the Hausdorff dimension of the sample paths of the solution is {d,1/H} and that the Hausdorff dimension of the level set Lₓ={ t∈[ε,1]: Xₜ=x} is 1-dH with positive probability when d<1/H
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