Brownian motion and Dirichlet problems at infinity
Hsu, Elton P.
Ann. Probab., Tome 31 (2003) no. 1, p. 1305-1319 / Harvested from Project Euclid
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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.
Publié le : 2003-07-14
Classification:  Brownian motion,  Dirichlet problem,  Cartan--Hadamard manifold.,  58J65,  60J60 
@article{1055425781,
     author = {Hsu, Elton P.},
     title = {Brownian motion and Dirichlet problems at infinity},
     journal = {Ann. Probab.},
     volume = {31},
     number = {1},
     year = {2003},
     pages = { 1305-1319},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1055425781}
}

Hsu, Elton P. Brownian motion and Dirichlet problems at infinity. Ann. Probab., Tome 31 (2003) no. 1, pp.  1305-1319. http://gdmltest.u-ga.fr/item/1055425781/