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Deviations from monotonicity of a Wiener process with drift

Published online by Cambridge University Press:  14 July 2016

P. J. Brockwell
P. J. Brockwell*
Affiliation:
Michigan State University
*
*Now at La Trobe University.
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Abstract

If X(t) is a Wiener process with EX(t) = vt and var X(t) = σ2t (where v > 0) and if M(t) = max0≦τ≦tX(τ) and Ta is the time of first passage through level a (where a > 0) we show that where is the coefficient of variation of Ta. Applications of the result to the “maturity-time” representation of cell-growth and to queues with heavy traffic are discussed.

Keywords

WIENER PROCESS WITH DRIFTRANDOM WALKWEAK CONVERGENCECELL-GROWTHQUEUES WITH HEAVY TRAFFIC
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 206 - 210
Copyright
Copyright © Applied Probability Trust 1974 

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Footnotes

Research supported by Air Force Office of Scientific Research under AFOSR Contract F44620–67–C–0049 in the Department of Mathematics, Stanford University.

References

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