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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.

Information

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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References

1Kac, M. and Luttinger, J. M.. Bose-Einstein condensation in the presence of impurities II. J. Math. Phys. 15 (1974), 183–186.CrossRefGoogle Scholar
2Varadhan, S. R. S.. Large deviations and applications, CBMS-NSF, Regional Conference Series in Applied Mathematics 46 (Philadelphia: SIAM, 1984).CrossRefGoogle Scholar
3M. Kac. Integration in function spaces and some of its applications, Lezione Fermiane, Accademia Nazionale dei Lincei Scuola Normale Superiore, Pisa, 1980.Google Scholar
4Kennedy, D. P.. The distribution of the maximum brownian excursion. J. Appl. Probab. 13 (1976), 371–376.CrossRefGoogle Scholar
5Chung, K. L.. Excursions in brownian motion. Ark. Mat. 14 (1976), 155–177.CrossRefGoogle Scholar
6Kuiper, N. H.. On the random cumulative frequency distribution. Nederl. Akad. Wetensch. Indag. Math. 22 (1960), 32–37.CrossRefGoogle Scholar
7Kuiper, N. H.. Tests concerning random points on a circle. Nederl. Akad. Wetensch. Indag. Math. 22 (1960), 38–47.CrossRefGoogle Scholar
8Biane, P. and Yor, M.. Cauchy's principal value and linear brownian motion (preprint, 1986).Google Scholar