Sojourns of Stationary Gaussian Processes over a Random Interval
Krzysztof Dȩbicki, Xiaofan Peng · Latin American Journal of Probability and Mathematical Statistics · 2023
We investigate asymptotics of the tail distribution of sojourn timeas u → ∞, where X is a centered stationary Gaussian process and T is an independent of X nonnegative random variable.The heaviness of the tail distribution of T impacts the form of the asymptotics, leading to four scenarios: the case of integrable T , the case of regularly varying T with index λ = 1 and index λ ∈ (0, 1) and the case of slowly varying tail distribution of T .The derived findings are illustrated by the analysis of the class of fractional Ornstein-Uhlenbeck processes.