Carolin Forster | Searcharxiv

arXiv2026

Asymptotic behavior of spatio-temporal point processes of exceedances

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.

math.PR↗

arXiv2022

Non-stationary max-stable models with an application to heavy rainfall data

In recent years, parametric models for max-stable processes have become a popular choice for modeling spatial extremes because they arise as the asymptotic limit of rescaled maxima of independent and identically distributed random processes. Apart from few exceptions for the class of extremal-t processes, existing literature mainly focuses on models with stationary dependence structures. In this paper, we propose a novel non-stationary approach that can be used for both Brown-Resnick and extremal-t processes - two of the most popular classes of max-stable processes - by including covariates in the corresponding variogram and correlation functions, respectively. We apply our new approach to extreme precipitation data in two regions in Southern and Northern Germany and compare the results to existing stationary models in terms of Takeuchi's information criterion (TIC). Our results indicate that, for this case study, non-stationary models are more appropriate than stationary ones for the region in Southern Germany. In addition, we investigate theoretical properties of max-stable processes conditional on random covariates. We show that these can result in both asymptotically dependent and asymptotically independent processes. Thus, conditional models are more flexible than classical max-stable models.

stat.ME↗