Self-similarity and fractional Brownian motions on Lie groups
Self-similarity and fractional Brownian motions on Lie groups
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李群上的自相似性和分数布朗运动
DOI：
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发表时间：
2006
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
本文的目的是定义和研究李群上分数布朗运动的概念。我们把它定义为由线性分数布朗运动驱动的随机微分方程的解。我们证明了该过程具有平稳增量并满足局部自相似性质。进一步对具有这种自相似性质的李群进行了刻画。最后，我们证明了路径群空间上的分部积分公式，并推导了密度的存在性。
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.