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One-sided excursions of brownian motion, and an application

Published online by Cambridge University Press:  14 July 2016

J. P. Imhof
J. P. Imhof*
Affiliation:
University of Geneva
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Abstract

The value of a process on C[0,∞) when it starts its first one-sided excursion of width ≧ α is related to first hitting one of two boundaries. Explicit results for brownian motion are applied to a finite dam model.

Keywords

BROWNIAN MOTIONFIRST PASSAGEFINITE DAM
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 635 - 638
Copyright
Copyright © Applied Probability Trust 1978 

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References

Feller, W. (1968) An Introduction to Probability Theory and its Applications, Vol. 1, 3rd edn. Wiley, New York.Google Scholar
Imhof, J. P. (1974) Oscillations of monotone amplitude and application. Transactions of the 7th Prague conference and 1974 EMS. Google Scholar
Kennedy, D. P. (1973) Limit theorems for finite dams. Stoch. Proc. Appl. 1, 269–278.CrossRefGoogle Scholar
Phatarfod, R. M., Speed, T. P. and Walker, M. (1971) A note on random walks. J. Appl. Prob. 8, 198–201.Google Scholar