Range of fluctuation of Brownian motion on a complete Riemannian manifold
成果类型：
Article
署名作者：
Grigor'yan, A; Kelbert, M
署名单位：
Imperial College London
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1998
页码：
78-111
关键词：
摘要：
We investigate the escape rate of the Brownian motion W-x(t) on a complete noncompact Riemannian manifold. Assuming that the manifold has at most polynomial volume growth and that its Ricci curvature is bounded below, we prove that dist(W-x(t), x) less than or equal to root Ct log t for all large t with probability 1. On the other hand, if the Ricci curvature is nonnegative and the volume growth is at least polynomial of the order n > 2, then dist(W-x(t), x) greater than or equal to root Ct/log(1/(n-2) t log log(2+epsilon)/(n-2))t, again for all large t with probability 1 (where epsilon > 0).