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Estimates for the expected lifetime of conditioned Brownian motion

Published online by Cambridge University Press:  18 September 2007

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

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 5 , October 2007 , pp. 1091 - 1099
Copyright
2007 Royal Society of Edinburgh

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