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On the time spent above a level by Brownian motion with negative drift

Published online by Cambridge University Press:  01 July 2016

J.-P. Imhof
J.-P. Imhof*
Affiliation:
University of Geneva
*
∗Postal address: Section de Mathématiques, Université de Genève 2–4, rue du Lièvre, Case Postale 240, 1211 Genève 24, Switzerland.
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Abstract

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Limit theorems of Berman involve the total time spent by Brownian motion with negative drift above a fixed or exponentially distributed negative level. We give explicitly the probability densities and distribution functions, obtained via an equivalence of laws.

Keywords

LAST PASSAGEDURATION OF POSITIVITY
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 18 , Issue 4 , December 1986 , pp. 1017 - 1018
Copyright
Copyright © Applied Probability Trust 1986 

References

1. Berman, S. M. (1982) Sojourns and extremes of a diffusion process on a fixed interval. Adv. Appl. Prob. 14, 811–832.Google Scholar
2. Imhof, J. P. and Kümmerling, P. (1986) Operational derivation of some Brownian motion results. Int. Statist. Rev. 54, to appear.Google Scholar