Self-similarity and fractional Brownian motions on Lie groups
Probability
2007-05-23 v1
Abstract
The goal of this paper is to define and study a notion of fractional Brownian motion on a Lie group. We define it as at the solution of a stochastic differential equation driven by a linear fractional Brownian motion. We show that this process has stationary increments and satisfies a local self-similar property. Furthermore the Lie groups for which this self-similar property is global are characterized. Finally, we prove an integration by parts formula on the path group space and deduce the existence of a density.
Keywords
Cite
@article{arxiv.math/0603199,
title = {Self-similarity and fractional Brownian motions on Lie groups},
author = {F. Baudoin and L. Coutin},
journal= {arXiv preprint arXiv:math/0603199},
year = {2007}
}