Self-similarity and fractional Brownian motions on lie groups

TY - JOUR

T1 - Self-similarity and fractional Brownian motions on lie groups

AU - Baudoin, Fabrice

AU - Coutin, Laure

PY - 2008/1/1

Y1 - 2008/1/1

N2 - 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.

AB - 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.

KW - Fractional Brownian motion

KW - Lie group

UR - http://www.scopus.com/inward/record.url?scp=48449083110&partnerID=8YFLogxK

U2 - 10.1214/EJP.v13-530

DO - 10.1214/EJP.v13-530

M3 - Journal article

AN - SCOPUS:48449083110

SN - 1083-6489

VL - 13

SP - 1120

EP - 1139

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

ER -