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)2β ≥ KM(x) ≤ -α(α- 1)/r(x)2 (α > β+ 2 > 2), respectively.
Original language | English (US) |
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Pages (from-to) | 1305-1319 |
Number of pages | 15 |
Journal | Annals of Probability |
Volume | 31 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2003 |
Keywords
- Brownian motion
- Cartan-Hadamard manifold
- Dirichlet problem
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty