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2008 Self-similarity and fractional Brownian motion on Lie groups
Fabrice Baudoin, Laure Coutin
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Electron. J. Probab. 13: 1120-1139 (2008). DOI: 10.1214/EJP.v13-530

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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Fabrice Baudoin. Laure Coutin. "Self-similarity and fractional Brownian motion on Lie groups." Electron. J. Probab. 13 1120 - 1139, 2008. https://doi.org/10.1214/EJP.v13-530

Information

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

zbMATH: 1189.60083
MathSciNet: MR2424989
Digital Object Identifier: 10.1214/EJP.v13-530

Subjects:
Primary: 60G15
Secondary: 60G18

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