Electronic Journal of Probability
- Electron. J. Probab.
- Volume 13 (2008), paper no. 38, 1120-1139.
Self-similarity and fractional Brownian motion on Lie groups
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.
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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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