Self-similarity and fractional Brownian motion on Lie groups
Fabrice Baudoin, Institut de mathématiques, Toulouse
Laure Coutin, Universite Paris 5
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.
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