The first exit time of a Brownian motion from an unbounded convex domain

• Wenbo V. Li ^[1]
  1. [1] University of Delaware

     University of Delaware

     Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 31, Nº. 2, 2003, págs. 1078-1096
• Idioma: inglés
• DOI: 10.1214/aop/1048516546
• Texto completo no disponible (Saber más ...)
• Resumen

  • Consider the first exit time τD of a (d+1)-dimensional Brownian motion from an unbounded open domain D=\set(x,y)∈\Rd+1\dvtxy>f(x),x∈\Rd starting at\vspace{0.5pt} (x0,f(x0)+1)∈\Rd+1 for some x0∈\Rd, where the function f(x) on \Rd is convex and f(x)→∞ as the Euclidean norm |x|→∞. Very general estimates for the asymptotics of log\prτD>t are given by using Gaussian techniques. In particular, for f(x)=exp{|x|p}, p>0, limt→∞t−1(logt)2/plog\prτD>t=−j2ν/2, where ν=(d−2)/2 and jν is the smallest positive zero of the Bessel function Jν.