Asymptotics of running maxima for φ-subgaussian random double arrays
share
The article studies the running maxima Y_m,j=max_1 ≤ k ≤ m, 1 ≤ n ≤ j X_k,n - a_m,j where {X_k,n, k ≥ 1, n ≥ 1} is a double array of φ-subgaussian random variables and {a_m,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.
READ FULL TEXT