Poisson limit theorem for the number of excursions above high and medium levels by Gaussian stationary sequences

TL;DR

This paper investigates the asymptotic distribution of the number of excursions above certain levels in Gaussian stationary sequences, showing they can be approximated by a Poisson cluster process.

Contribution

It provides a new Poisson limit theorem for the count of excursions in Gaussian stationary sequences, extending previous results to high and medium levels.

Findings

Poisson cluster process approximates excursions above levels

Asymptotic behavior characterized for high and medium levels

Extension of limit theorems to Gaussian sequences

Abstract

Asymptotic behavior of the point process of high and medium values of a Gaussian stationary process with discrete time is considered. An approximation by a Poisson cluster point process is given for the point process.