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

Abstract

Let $\{X(t):t\in [0,\infty )\}$ be a centered Gaussian process with stationary increments and variance function ${\sigma }_X^2(t)$. We study the exact asymptotics of $\mathbb{P}({\sup }_{t\in [0,T]}X(t)>u)$ as $u\to \infty$, 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.

Published in at http://dx.doi.org/10.3150/10-BEJ266 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (1)

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