%0 Journal Article
%T Tail Asymptotics of Supremum of Certain Gaussian Processes over Threshold Dependent Random Intervals
%A Krzysztof DŁżbicki
%A Enkelejd Hashorva
%A Lanpeng Ji
%J Mathematics
%D 2013
%I arXiv
%X Let $\{X(t),t\ge0\}$ 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.
%U http://arxiv.org/abs/1311.5919v1