On conservation of probability and the Feller property

• 成果类型: Article
• 署名作者: Qian, ZM
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1996
• 页码: 280-292
• 关键词: complete riemannian manifold; brownian-motion; heat kernel

摘要

It is known that any smooth, nondegenerate, second-order elliptic operator on a manifold (dimension not equal 2) has the form Delta + B, where B is a vector field and Delta is the Laplace-Beltrami operator under some Riemannian metric on the manifold. In this paper we give several conditions on the ''Ricci curvature'' Ric - del(B)(8) associated with the operator Delta + B to ensure that the diffusion semigroup generated by Delta + B conserves probability and possesses the Feller property.