Brownian motion and Dirichlet problems at infinity

• 成果类型: Article
• 署名作者: Hsu, EP
• 署名单位: Northwestern University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1055425781
• 发表日期: 2003
• 页码: 1305-1319
• 关键词: negatively curved manifolds; harmonic-functions; CURVATURE

摘要

We discuss angular convergence of Riemannian Brownian motion on a Cartan-Hadamard manifold and show that the Dirichlet problem at infinity for such a manifold is uniquely solvable under the curvature conditions -Ce(2-eta)ar(x) less than or equal to K-M(x) less than or equal to -a(2) (eta > 0) and -Cr(x)(2beta) less than or equal to K-M(x) less than or equal to -alpha(alpha - 1)/r(x)(2) (alpha > beta + 2 > 2), respectively.