Self-similarity and fractional Brownian motion on Lie groups

Fabrice Baudoin (Institut de mathématiques, Toulouse)
Laure Coutin (Universite Paris 5)


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.

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Pages: 1120-1139

Publication Date: July 22, 2008

DOI: 10.1214/EJP.v13-530


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