Exact asymptotics of supremum of a stationary Gaussian process over a random interval

Marek Arendarczyk, Krzysztof Debicki

Let $\{X(t):t\in [0,\infty )\}$ be a centered stationary Gaussian process. We study the exact asymptotics of $\pr (\sup_{s \in [0,T]} X(t) > u)$, as $u\to \infty$, where $T$ i…