The supremum of a Gaussian process over a random interval

Krzystof Debicki, Bert Zwart and Sem Borst

Statistics & Probability Letters, 2004, vol. 68, issue 3, 221-234

Abstract: The aim of this note is to give the exact asymptotics ofwhere {X(t): t[greater-or-equal, slanted]0} is a centered Gaussian process with stationary increments and T is an independent non-negative random variable with regularly varying tail distribution. In addition, we obtain explicit lower and upper bounds for the prefactor. As an example we analyze the case of X(t) being a fractional Brownian motion and a Gaussian integrated process.

Keywords: Exact; asymptotics; Extremes; Fractional; Brownian; motion; Gaussian; process; Regular; variation (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (2)

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