Flots et series de Taylor stochastiques
Flots et series de Taylor stochastiques
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泰勒随机花型和系列
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
G. B. Arous
中科院分区：
文献类型：
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作者：
G. B. Arous
摘要研究了一类随机微分方程解的展开式，将其表示为一系列随机（Stratonovitch）积分的（无穷）和。这使我们能够给出一个普遍的和明确的公式，任何不变的扩散李群的李括号，以及一个普遍的和明确的公式布朗运动的黎曼流形的导数的曲率张量。其中第一个公式包含并推广到非幂零情形，Doss [6]，Sussmann [17]，Yamato [18]，Fliess和Normand-Cyrot [7]，Krener和Lobry [19]以及Kunita [11]关于随机微分方程解的表示的结果。
SummaryWe study the expansion of the solution of a stochastic differential equation as an (infinite) sum of iterated stochastic (Stratonovitch) integrals. This enables us to give a universal and explicit formula for any invariant diffusion on a Lie group in terms of Lie brackets, as well as a universal and explicit formula for the brownian motion on a Riemannian manifold in terms of derivatives of the curvature tensor. The first of these formulae contains, and extends to the non nilpotent case, the results of Doss [6], Sussmann [17], Yamato [18], Fliess and Normand-Cyrot [7], Krener and Lobry [19] and Kunita [11] on the representation of solutions of stochastic differential equations.