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Some remarks on Brownian motion with drift

Published online by Cambridge University Press:  14 July 2016

R. A. Doney  and
D. R. Grey
R. A. Doney*
Affiliation:
University of Manchester
D. R. Grey*
Affiliation:
University of Sheffield
*
∗Postal address: Statistical Laboratory, Department of Mathematics, The University, Manchester M13 0PL, UK.
∗∗Postal address: Department of Probability and Statistics, The University, Sheffield S3 7RH, UK.
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Abstract

Certain limit theorems due to Berman involve the total time spent by Brownian motion with positive drift below an independent exponentially distributed level. Imhof has calculated the density function and shown that this random variable has two interesting probabilistic properties. We give sample path arguments which explain these two facts.

Keywords

PATH DECOMPOSITIONTIME BELOW A LEVEL
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 659 - 663
Copyright
Copyright © Applied Probability Trust 1989 

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References

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