Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Table of Contents - 2007 - Volume 137, Issue 05  


Estimates for the expected lifetime of conditioned Brownian motion

M. van den Berg a1, A. Dall' Acqua a2 and G. H. Sweers a3
a1 Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK (m.vandenberg@bris.ac.uk)
a2 Mathematisches Institut, Universität München, Theresienstraβe 39, 80333 München, Germany
a3 Mathematisches Institut, Universität Köln, Weyertal 86–90, 50931 Köln, Germany

Article author query
van den berg m   [Google Scholar] 
dall acqua a   [Google Scholar] 
sweers gh   [Google Scholar] 
 

Abstract

Let $\tau_\varOmega$ denote the lifetime of Brownian motion in an open connected set $\varOmega\subset\mathbb{R}^m$. We obtain the asymptotic behaviour of the expected lifetime $\mathbb{E}_x^y[\tau_\varOmega]$ as $y\to x$, where the Brownian motion is conditioned to start at $x$ and to exit $\varOmega\setminus\{y\}$ at $\{y\}$.

(Received April 11 2006)
(Accepted August 16 2006)