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July 2003 Brownian motion and Dirichlet problems at infinity
Elton P. Hsu
Ann. Probab. 31(3): 1305-1319 (July 2003). DOI: 10.1214/aop/1055425781


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 $-Ce^{(2-\eta) ar(x)}\le K_M(x)\le-a^2$\vspace*{0.5pt} ($\eta>0$) and $-Cr(x)^{2\beta} \le K_M(x)\le - \alpha (\alpha-1)/r(x)^2$ ($\alpha>\beta+2>2$), respectively.


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Elton P. Hsu. "Brownian motion and Dirichlet problems at infinity." Ann. Probab. 31 (3) 1305 - 1319, July 2003.


Published: July 2003
First available in Project Euclid: 12 June 2003

zbMATH: 1054.58027
MathSciNet: MR1988474
Digital Object Identifier: 10.1214/aop/1055425781

Primary: 58J65
Secondary: 60J60

Keywords: Brownian motion , Cartan--Hadamard manifold. , Dirichlet problem

Rights: Copyright © 2003 Institute of Mathematical Statistics

Vol.31 • No. 3 • July 2003
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