RADIAL PART OF BROWNIAN-MOTION ON A RIEMANNIAN MANIFOLD
成果类型：
Article
署名作者：
LIAO, M; ZHENG, WA
署名单位：
University of California System; University of California Irvine
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176988382
发表日期：
1995
页码：
173-177
关键词：
摘要：
Let rho(t) be the radial part of a Brownian motion in an n-dimensional Riemannian manifold M starting at x and let T = T-epsilon be the first time t when rho(t) = epsilon. We show that E[rho(t boolean AND T)(2)] = nt - (1/6)S(x)t(2) + o(t(2)), as t down arrow 0, where S(x) is the scalar curvature. The same formula holds for E[rho(t)(2)] under some boundedness condition on M.