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

By Marek Arendarczyk, Krzysztof Dcebicki. 2009

59 citations recorded by the source corpus.

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.

Subfields: Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/76feb2cd09ed3ca9af0aa3fb84c6f9a1ab1120c6

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Citations in the corpus

Tail asymptotics of supremum of certain Gaussian processes over threshold dependent random intervals (2013, methodology): “In the case that {Y (t), t ≥ 0} is a Gamma process and c = 0, investigation of ψT (u), as u→ ∞ reduces to the analysis of the tail asymptotics of the fractional Laplace motion; see Kozubowski et al. (2006), Arendarczyk and Dȩbicki (2011).”
Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures (2016, background): “Lemma 6 (Tail decay of products of Weibull-type variables; Arendarczyk and Debicki, 2011) .”