Arendarczyk, Marek; Dȩbicki, Krzysztof - In: Statistics & Probability Letters 82 (2012) 3, pp. 645-652
Let {X(t):t∈[0,∞)} be a centered stationary Gaussian process. We study the exact asymptotics of P(sups∈[0,T]X(s)u), as u→∞, where T is an independent of {X(t)} nonnegative random variable. It appears that the heaviness of T impacts the form of the asymptotics, leading to three...