Electronic Journal of Probability

Self-similarity and fractional Brownian motion on Lie groups

Fabrice Baudoin and Laure Coutin

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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.

Article information

Electron. J. Probab., Volume 13 (2008), paper no. 38, 1120-1139.

Accepted: 22 July 2008
First available in Project Euclid: 1 June 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G15: Gaussian processes
Secondary: 60G18: Self-similar processes

Fractional Brownian motion Lie group

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Baudoin, Fabrice; Coutin, Laure. Self-similarity and fractional Brownian motion on Lie groups. Electron. J. Probab. 13 (2008), paper no. 38, 1120--1139. doi:10.1214/EJP.v13-530. https://projecteuclid.org/euclid.ejp/1464819111

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