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Self-similarity and fractional Brownian motions on Lie groups
- Source :
- Electronic Journal of Probability, Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2008, 13 (38), pp.1120-1139, Electronic Journal of Probability, 2008, 13 (38), pp.1120-1139
- Publication Year :
- 2008
- Publisher :
- HAL CCSD, 2008.
-
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. Finally, we prove an integration by parts formula on the path group space and deduce the existence of a density.
Details
- Language :
- English
- ISSN :
- 10836489
- Database :
- OpenAIRE
- Journal :
- Electronic Journal of Probability, Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2008, 13 (38), pp.1120-1139, Electronic Journal of Probability, 2008, 13 (38), pp.1120-1139
- Accession number :
- edsair.doi.dedup.....f076670e0796e1b4ca39b82c5f51fa37