Asymptotic expansion of stochastic flows
Asymptotic expansion of stochastic flows
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随机流的渐近展开
DOI：
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发表时间：
1993
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通讯作者：
F. Castell
中科院分区：
文献类型：
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作者：
F. Castell
研究了一类随机微分方程解的小时间渐近展开式。利用李括号和迭代随机Stratonovich积分得到了一个普适的显式公式。这个公式包含了Doss [6]，Sussmann [15]，Fliess和Normand-Cyrot [7]，Krener和Lobry [10]，Yamato [17]和Kunita [11]在幂零情形下的结果，并将Ben Arous [3]给出的李群上不变扩散的表示推广到一般扩散。主要的工具是确定性常微分方程的渐近展开，由Schlahartz [14]给出。
SummaryWe study the asymptotic expansion in small time of the solution of a stochastic differential equation. We obtain a universal and explicit formula in terms of Lie brackets and iterated stochastic Stratonovich integrals. This formula contains the results of Doss [6], Sussmann [15], Fliess and Normand-Cyrot [7], Krener and Lobry [10], Yamato [17] and Kunita [11] in the nilpotent case, and extends to general diffusions the representation given by Ben Arous [3] for invariant diffusions on a Lie group. The main tool is an asymptotic expansion for deterministic ordinary differential equations, given by Strichartz [14].