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On the asymptotics of a Wiener integral

Published online by Cambridge University Press:  14 November 2011

M. van den Berg  and
J. T. Lewis
M. van den Berg
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, U.K.
J. T. Lewis
Affiliation:
Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Republic of Ireland
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Synopsis

Let mt(ω) be the range of a standard brownian bridge on R with ω(0) = ω(t) = 0 and let µt(ω) be the corresponding Wiener measure. We determine the asymptotic behaviour for large t of ∫ e−G(mt(ω)) µt(dω) for an increasing convex function G.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 105 , Issue 1 , 1987 , pp. 195 - 198
Copyright
Copyright © Royal Society of Edinburgh 1987

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