Brownian motion and Dirichlet problems at infinity

• Elton P. Hsu ^[1]
  1. [1] Northwestern University

     Northwestern University

     Township of Evanston, Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 31, Nº. 3, 2003, págs. 1305-1319
• Idioma: inglés
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• Resumen

  • 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\vspace*{0.5pt} (η>0) and −Cr(x)2β≤KM(x)≤−α(α−1)/r(x)2 (α>β+2>2), respectively.