Extreme value theory for space-time with random coefficients

Saliou Diouf and Yentchabaré Kolani

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 5, 1736-1744

Abstract: In this paper, we study the extreme value behavior of the space-time process given by Xi(t)=∑j≥1Ψij(t)Zi−j(t),t∈[0,1],i∈Z. We assume that {Zi(t)}t∈[0,1],i∈Z is a sequence of i.i.d random fields on [0,1] with values in the Skorokhod space D[0,1] of càdlàg functions (i.e., right-continuous functions with left limits) D[0,1] equipped with the J1 topology. The coefficients {Ψij(t)}t∈[0,1],i∈Z are processes with continuous sample paths.Our first aim is to establish a limit theory for point processes based on X(t). Secondly, using point processes, we study the limiting distribution of the normalized maximum process {an−1 max1≤i≤nXi(t)}t∈[0,1]. The result obtained in the second step can be viewed as extension of Balan who postponed the study of the behavior of maxima. It can also be considered as a generalization of Davis and Mikosch from deterministic real coefficients to random coefficients (Ψij)i≥1.

Date: 2024
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DOI: 10.1080/03610926.2022.2109676

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