Exact asymptotics of supremum of a stationary Gaussian process over a random interval

Marek Arendarczyk and Krzysztof Dȩbicki

Statistics & Probability Letters, 2012, vol. 82, issue 3, 645-652

Abstract: Let {X(t):t∈[0,∞)} be a centered stationary Gaussian process. We study the exact asymptotics of P(sups∈[0,T]X(s)>u), as u→∞, where T is an independent of {X(t)} nonnegative random variable. It appears that the heaviness of T impacts the form of the asymptotics, leading to three scenarios: the case of integrable T, the case of T having regularly varying tail distribution with parameter λ∈(0,1) and the case of T having slowly varying tail distribution.

Keywords: Asymptotics; Gaussian process; Supremum distribution (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.spl.2011.11.015

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