Sunset over Brownistan

Erhan Çinlar

Stochastic Processes and their Applications, 1992, vol. 40, issue 1, 45-53

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.

Keywords: Brownian; motion; concave; majorant; maximum; of; Brownian; motion; with; drift; spatial; distribution; in; queues (search for similar items in EconPapers)
Date: 1992
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