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Asymptotics of Running Maxima for φ-Subgaussian Random Double Arrays

Author

Listed:
  • 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)

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.

Suggested Citation

  • Nour Al Hayek & Illia Donhauzer & Rita Giuliano & Andriy Olenko & Andrei Volodin, 2022. "Asymptotics of Running Maxima for φ-Subgaussian Random Double Arrays," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1341-1366, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09866-6
    DOI: 10.1007/s11009-021-09866-6
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    References listed on IDEAS

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    1. Csáki, Endre & Gonchigdanzan, Khurelbaatar, 2002. "Almost sure limit theorems for the maximum of stationary Gaussian sequences," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 195-203, June.
    2. Yuriy Kozachenko & Andriy Olenko & Olga Polosmak, 2015. "Convergence in L p ([0, T]) of Wavelet Expansions of φ-Sub-Gaussian Random Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 139-153, March.
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