Fine properties of fractional Brownian motions on Wiener space

Author: 

Qian, Z
Jiawei, J

Publication Date: 

18 December 2018

Journal: 

Journal of Mathematical Analysis and Applications

Last Updated: 

2020-01-21T14:17:06.117+00:00

Issue: 

1

Volume: 

473

DOI: 

10.1016/j.jmaa.2018.12.039

page: 

141-173

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 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.

Symplectic id: 

952216

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article