Methodology and Computing in Applied Probability ( IF 1.0 ) Pub Date : 2021-05-03 , DOI: 10.1007/s11009-021-09866-6 Nour Al Hayek , Illia Donhauzer , Rita Giuliano , Andriy Olenko , Andrei Volodin
The article studies the running maxima \(Y_{m,j}=\max_{1 \le k \le m, 1 \le n \le j} X_{k,n} - a_{m,j}\) 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.
中文翻译:
φ-高斯随机双阵列的极大值的渐近性。
本文研究了运行的最大值\(Y_ {m,j} = \ max_ {1 \ le k \ le m,1 \ le n \ le j} X_ {k,n}-a_ {m,j} \)其中{ X ķ,ñ,ķ ≥1,ñ ≥1}是一个双阵列φ -subgaussian随机变量和{一米,Ĵ,米≥1,Ĵ ≥1}是常数的双阵列。的{正和负部分的双阵列的最大值的渐近ÿ米,Ĵ,米≥1,Ĵ ≥1}进行了研究,当{ X ķ,Ñ,ķ≥1,Ñ ≥1}具有合适的“指数型”尾分布。针对各种重要的特定情况和φ-高斯随机变量的类别指定了主要结果。