Asymptotics of Running Maxima for φ-Subgaussian Random Double Arrays

Nour Al Hayek (), Illia Donhauzer (), Rita Giuliano (), Andriy Olenko () and Andrei Volodin ()
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Nour Al Hayek: University of Regina
Illia Donhauzer: La Trobe University
Rita Giuliano: Università di Pisa
Andriy Olenko: La Trobe University
Andrei Volodin: University of Regina

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 3, 1341-1366

Abstract: Abstract The article studies the running maxima Y m , j = max 1 ≤ k ≤ m , 1 ≤ n ≤ j X k , n − a m , j $Y_{m,j}=\max_{1 \le k \le m, 1 \le n \le j} X_{k,n} - a_{m,j}$ where {Xk,n,k ≥ 1,n ≥ 1} is a double array of φ-subgaussian random variables and {am,j,m ≥ 1,j ≥ 1} is a double array of constants. Asymptotics of the maxima of the double arrays of positive and negative parts of {Ym,j,m ≥ 1,j ≥ 1} are studied, when {Xk,n,k ≥ 1,n ≥ 1} have suitable “exponential-type” tail distributions. The main results are specified for various important particular scenarios and classes of φ-subgaussian random variables.

Keywords: Random double array; Running maxima; φ-subgaussian random variables; Almost sure convergence; 60F15; 60G70; 60G60 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09866-6

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