An Introduction to Stochastic Differential Equations on Manifolds
An Introduction to Stochastic Differential Equations on Manifolds
复制标题
流形上的随机微分方程简介
DOI：
10.1007/978-94-010-2675-8_4
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发表时间：
1973
影响因子：
1.7
通讯作者：
J. M. C. Clark
中科院分区：
文献类型：
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作者：
J. M. C. Clark
这些注释介绍了与理解和精确描述由白噪声驱动的动力系统的概念有关的数学工具。主要工具是伊藤的随机积分和随机微分方程；然而，Fisk和Stratonovich的表示也被包括在内，不仅因为他们有很好的物理解释，而且因为他们似乎为流形上的过程提供了一种自然的形式主义。有些地方的处理是粗略的，但我们至少试图给出主要论点的要点。基本的参考文献有Ito [1,2,3]， McKean[4]和Wong[5]。
These notes introduce the mathematical apparatus that is relevant for an understanding and precise description of the idea of a dynamical system driven by white noise. The main tools are the stochastic integral and stochastic differential equations of Ito; however the representations of Fisk and Stratonovich are also included, not only because they have a nice physical interpretation, but because they seem to provide a natural formalism for processes that lie on manifolds. The treatment is sketchy in places but we have tried to give at least the gist of the main arguments. Basic references are Ito [1,2,3] , McKean[4] and Wong [5].