Asymptotics of supremum distribution of a Gaussian process over a Weibullian time

Abstract

Let {X(t) : t ε [0,∞)} be a centered Gaussian process with stationary increments and variance function σX2 (t). We study the exact asymptotics of ℙ(suptε[0,T ] X(t) > u) as u→∞, where T is an independent of {X(t)} non-negative Weibullian random variable. As an illustration, we work out the asymptotics of the supremum distribution of fractional Laplace motion. © 2011 ISI/BS.