%0 Journal Article
%T Self-similarity and fractional Brownian motions on Lie groups
%A F. Baudoin
%A L. Coutin
%J Mathematics
%D 2006
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0603199v1