Asymptotic behavior of spatio-temporal point processes of exceedances

TL;DR

This paper studies the long-term behavior of spatio-temporal exceedance events, modeling their distribution and convergence using advanced probabilistic frameworks for extreme values.

Contribution

It extends existing theories by analyzing the asymptotic behavior of exceedance point processes with site-dependent thresholds in a spatio-temporal context.

Findings

Proves weak convergence of the point processes of extremes.

Explicitly determines the limit distribution of the exceedance process.

Extends the framework of stationary regularly varying multivariate time series.

Abstract

In this paper, we analyze the asymptotic behavior of the point process of exceedances in a spatio-temporal setting whose points are given by the rescaled occurrence times, the sites and the rescaled values of exceedances. Here, the exceedances over a high threshold are flexibly defined via site-dependent risk functionals. Exploiting the framework of stationary regularly varying multivariate time series, we merge and extend the results from the literature in order to show weak convergence of the considered point processes of extremes and to explicitly determine its limit distribution.