Fine properties of fractional Brownian motions on Wiener space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:473

Article

Li, Jiawei¹  Qian, Zhongmin¹ 

[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England

关键词: Capacity;    Fractional Brownian motion;    Malliavin derivative;    Sample property;   

DOI  :  10.1016/j.jmaa.2018.12.039

来源: Elsevier

【 摘 要 】

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 Ustunel, and show non-differentiability, modulus of continuity, law of the 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free