Hostname: page-component-7dc689bd49-6c8t5 Total loading time: 0 Render date: 2023-03-20T09:04:14.139Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

Estimates for the expected lifetime of conditioned Brownian motion

Published online by Cambridge University Press:  18 September 2007

M. van den Berg
Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK (
A. Dall' Acqua
Mathematisches Institut, Universität München, Theresienstraβe 39, 80333 München, Germany
G. H. Sweers
Mathematisches Institut, Universität Köln, Weyertal 86–90, 50931 Köln, Germany


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 $\{y\}$.

Research Article
2007 Royal Society of Edinburgh

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)