精品文档---下载后可任意编辑中心对称流形上的布朗运动的开题报告题目：中心对称流形上的布朗运动摘要：本文主要讨论中心对称流形上的布朗运动。首先介绍了中心对称流形的基本概念，包括定义、性质以及中心对称群的作用。然后对布朗运动的概念进行了简单的回顾，并引入了中心对称流形上的布朗运动的定义。接着讨论了中心对称流形上的布朗运动的一些性质，包括随机微分方程的解及其期望、矩、共轭过程等。最后，给出了一些未来讨论的方向，包括拓展到非紧流形、考虑布朗运动与其他随机过程的关系等。关键词：中心对称流形、布朗运动、随机微分方程、共轭过程、非紧流形Abstract: This paper mainly studies Brownian motion on central symmetric manifolds. Firstly, the basic concepts of central symmetric manifolds are introduced, including the definition, properties and the action of central symmetric group. Then, the concept of Brownian motion is briefly reviewed, and the definition of Brownian motion on central symmetric manifolds is introduced. The properties of Brownian motion on central symmetric manifolds are discussed, including the solution of stochastic differential equations and its expectation, moments, conjugate process, etc. Finally, some future research directions are given, including extending to non-compact manifolds, considering the relationship between Brownian motion and other stochastic processes, etc.Keywords: central symmetric manifold, Brownian motion, stochastic differential equation, conjugate process, non-compact manifold
