Fine properties of fractional Brownian motions on Wiener space

2018/07/06 by Li, Jiawei, Qian, Zhongmin
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1807.02540

Abstract

We study several important fine properties for the family of fractional Brownian motions with Hurst parameter H under the (p,r)-capacity on classical Wiener space introduced by Malliavin. We regard fractional Brownian motions as Wiener functionals via the integral representation discovered by Decreusefond and Üstünel, and show non differentiability, modulus of continuity, law of iterated Logarithm(LIL) and self-avoiding properties of fractional Brownian motion sample paths using Malliavin calculus as well as the tools developed in the previous work by Fukushima, Takeda and etc. for Brownian motion case.

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