黎曼曲面上布朗运动的局部平移正交不变性及其应用

Local Translation and Orthoconal In variances of Brownian Motiom on Riemann Surfaces and Their Application

本文将欧氏空间上布朗运动的平移,正交不变性推广到黎曼曲面上,得到局部成立的类似性质,并利用这些结果给出一种黎曼曲面上 Dirichlet问题的概率解法。

In this paper.the first part is mainly devoted to obtain the results that local translation and orthogonal invariances of Brownain motion on Riemann surfaces are true.The second part considering the application,using the results of first part,a probabilitic methord to solve Dirichlet problem on Riemann surfaces is given.