The supremum of a Gaussian process over a random interval

DOI10.1016/j.spl.2003.07.024zbMath1072.60032OpenAlexW2076362192MaRDI QIDQ1771422

Bert Zwart, Krzysztof Dȩbicki, Sem C. Borst

Publication date: 21 April 2005

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://ir.cwi.nl/pub/4211

zbMATH Keywords

fractional Brownian motionregular variationextremesexact asymptotics

Mathematics Subject Classification ID

Gaussian processes (60G15)

Related Items (16)

Some limit results on supremum of Shepp statistics for fractional Brownian motion ⋮ Large buffer asymptotics for generalized processor sharing queues with Gaussian inputs ⋮ Extrema of multi-dimensional Gaussian processes over random intervals ⋮ Exact tail asymptotics of the supremum of strongly dependent Gaussian processes over a random interval ⋮ Extremes of randomly scaled Gumbel risks ⋮ On the asymptotics of supremum distribution for some iterated processes ⋮ Asymptotic of the running maximum distribution of a Gaussian Bridge ⋮ Exact asymptotics of supremum of a stationary Gaussian process over a random interval ⋮ Asymptotics of supremum distribution of a Gaussian process over a Weibullian time ⋮ Exact asymptotics and limit theorems for supremum of stationary \(\chi\)-processes over a random interval ⋮ Extremes of Shepp statistics for fractional Brownian motion ⋮ On the first-passage times of certain Gaussian processes, and related asymptotics ⋮ Limit theorems for supremum of Gaussian processes over a random interval ⋮ Reduced-load equivalence for Gaussian processes ⋮ Subexponential asymptotics of hybrid fluid and ruin models ⋮ Tail Asymptotics of the Supremum of a Regenerative Process

Cites Work

• Subexponentiality of the product of independent random variables
• Sampling at subexponential times, with queueing applications
• An asymptotic formula for the distribution of the maximum of a Gaussian process with stationary increments
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