Asymptotics of Running Maxima for φ-Subgaussian Random Double Arrays
NA Hayek, I Donhauzer, R Giuliano, A Olenko… - … and Computing in …, 2022 - Springer
Methodology and Computing in Applied Probability, 2022•Springer
The article studies the running maxima Y m, j= max 1≤ k≤ m, 1≤ n≤ j X k, n− am, j where
{X k, 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 {Y m, j, m≥ 1, j≥ 1} are studied, when {X k, 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.
{X k, 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 {Y m, j, m≥ 1, j≥ 1} are studied, when {X k, 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.
Abstract
The article studies the running maxima 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.
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