Acta Mathematica Vietnamica
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Limit Theorems for the Number of Up-crossings of the Conjunction Set of Stationary Gaussian Processes
Viet-Hung Phampp. 401-413
Abstract
In this paper, we investigate the limit theorem for the number of up-crossings of the conjunction set of stationary Gaussian processes. We prove that as the level tends to infinity then the normalized point process of the number of up-crossings converges weakly to a standard Poisson process. Our proof is based on a discretization argument and a Normal comparison lemma for the order statistics.