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The supremum of a Gaussian process over a random interval

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.
Year of publication:
2004
Authors: Debicki, Krzystof ; Zwart, Bert ; Borst, Sem
Published in:
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 68.2004, 3, p. 221-234
Publisher: Elsevier
Keywords: Exact asymptotics Extremes Fractional Brownian motion Gaussian process Regular variation
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Type of publication: Article
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Persistent link: https://www.econbiz.de/10005223787
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