PROPERTIES AT INFINITY OF DIFFUSION SEMIGROUPS AND STOCHASTIC FLOWS VIA WEAK UNIFORM COVERS
PROPERTIES AT INFINITY OF DIFFUSION SEMIGROUPS AND STOCHASTIC FLOWS VIA WEAK UNIFORM COVERS
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DOI：
10.1007/bf01049807
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发表时间：
1994-12-01
影响因子：
1.1
通讯作者：
LI, XM
中科院分区：
文献类型：
--
作者：
LI, XM
本文统一地处理了H.Donnelly，P.Li和L.Schwartz关于给定紧化的开流形上热半群的性态的一些结果，以及与相关随机微分方程解在无穷远处的性态的关系。一个主要的工具是使用歧管的某些盖子：这也提供了非爆炸测试。作为推论，我们得到了关于Ricci曲率在距离函数中至多二次衰减的完备黎曼流形上布朗运动行为的已知结果。
A unified treatment is given of some results of H. Donnelly, P. Li and L. Schwartz concerning the behaviour of heat semigroups on open manifolds with given compactifications, on one hand, and the relationship with the behaviour at infinity of solutions of related stochastic differential equations on the other. A principal tool is the use of certain covers of the manifold: which also gives a non-explosion test. As a corollary we obtain known results about the behaviour of Brownian motions on a complete Riemannian manifold with Ricci curvature decaying at most quadratically in the distance function.