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Sunset over Brownistan

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  • Çinlar, Erhan

Abstract

Consider a Brownian motion with a downward drift of rate a. Its maximum over all time has the exponential distribution with parameter 2a. Our aim is to study this maximum as a stochastic process indexed by a. That process is related to the concave majorant of the standard Brownian motion and, through the latter, to a Poisson random measure. This connection is exploited to obtain distributional results. The results are of interest in queueing theory.

Suggested Citation

  • Çinlar, Erhan, 1992. "Sunset over Brownistan," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 45-53, February.
    • Handle: RePEc:eee:spapps:v:40:y:1992:i:1:p:45-53
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    Cited by:

    1. Giraud, Christophe, 2003. "On the convex hull of a Brownian excursion with parabolic drift," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 41-62, July.

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