HARNACK INEQUALITY FOR SDE WITH MULTIPLICATIVE NOISE AND EXTENSION TO NEUMANN SEMIGROUP ON NONCONVEX MANIFOLDS

• 成果类型: Article
• 署名作者: Wang, Feng-Yu
• 署名单位: Beijing Normal University; Swansea University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP600
• 发表日期: 2011
• 页码: 1449-1467
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; sobolev inequalities; time asymptotics; diffusion; PROPERTY

摘要

By constructing a coupling with unbounded time-dependent drift, dimension-free Harnack inequalities are established for a large class of stochastic differential equations with multiplicative noise. These inequalities are applied to the study of heat kernel upper bound and contractivity properties of the semigroup. The main results are also extended to reflecting diffusion processes on Riemannian manifolds with nonconvex boundary.