Self-similarity and fractional Brownian motion on Lie groups
Self-similarity and fractional Brownian motion on Lie groups
复制标题
李群上的自相似性和分数布朗运动
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
L. Coutin
中科院分区：
文献类型：
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作者：
Fabrice Baudoin;L. Coutin
本文的目标是定义和研究李群上分数布朗运动的概念。我们将其定义为由线性分数布朗运动驱动的随机微分方程的解。我们证明这个过程具有平稳增量并且满足局部自相似性质。此外，还对具有全局自相似性质的李群进行了表征。
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.