Tail Asymptotics of Supremum of Certain Gaussian Processes over Threshold Dependent Random Intervals

Abstract

Let $\{X(t),t\ge 0\}$ be a centered Gaussian process and let $\gamma$ be a non-negative constant. In this paper we study the asymptotics of $P\{\underset{t\in [0,\mathcal{T}/u^{\gamma }]}{\sup }X(t)>u\}$ as $u\to \infty$, with $\mathcal{T}$ an independent of $X$ non-negative random variable. As an application, we derive the asymptotics of finite-time ruin probability of time-changed fractional Brownian motion risk processes.

15 pages

References in corpus (1)

• On the Supremum of gamma-reflected Processes with Fractional Brownian Motion as Input

Cited by in corpus (1)

• On the Probability of Conjunctions of Stationary Gaussian Processes