Self-similarity and fractional Brownian motions on Lie groups

Details Self-similarity and fractional Brownian motions on Lie groups Self-similarity and fractional Brownian motions on Lie groups

2006-03-08

arxiv.org/abs/math/0603199v1

Mathematics

Probability

Scientific paper

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.

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