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

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

2009-09-21

arxiv.org/abs/0909.3667v2

Bernoulli 2011, Vol. 17, No. 1, 194-210

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/10-BEJ266 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ266

Let $\{X(t):t\in[0,\infty)\}$ be a centered Gaussian process with stationary increments and variance function $\sigma^2_X(t)$. 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.

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