Abstract
Let $\{X(t) :t∈[0, ∞)\}$ be a centered Gaussian process with stationary increments and variance function $σ_X^2(t)$. We study the exact asymptotics of $ℙ(\sup _{t∈[0, T]}X(t)>u)$ 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.
Citation
Marek Arendarczyk. Krzysztof Dȩbicki. "Asymptotics of supremum distribution of a Gaussian process over a Weibullian time." Bernoulli 17 (1) 194 - 210, February 2011. https://doi.org/10.3150/10-BEJ266
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