Brownian motion and Dirichlet problems at infinity

Elton P. Hsu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

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-η)ar(x) ≤ KM(X) ≤ -a2 (η > 0) and -Cr(x) ≥ KM(x) ≤ -α(α- 1)/r(x)2 (α > β+ 2 > 2), respectively.

Original languageEnglish (US)
Pages (from-to)1305-1319
Number of pages15
JournalAnnals of Probability
Volume31
Issue number3
DOIs
StatePublished - Jul 2003

Keywords

  • Brownian motion
  • Cartan-Hadamard manifold
  • Dirichlet problem

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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