On the maxima of suprema of dependent Gaussian models

Lanpeng Ji () and Xiaofan Peng ()
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Lanpeng Ji: University of Leeds
Xiaofan Peng: University of Electronic Science and Technology of China

Queueing Systems: Theory and Applications, 2023, vol. 105, issue 1, No 5, 99-128

Abstract: Abstract In this paper, we study the asymptotic distribution of the maxima of suprema of dependent Gaussian processes with trend. For different scales of the time horizon we obtain different normalizing functions for the convergence of the maxima. The obtained results not only have potential applications in estimating the delay of certain Gaussian fork-join queueing systems but also provide interesting insights to the extreme value theory for triangular arrays of random variables with row-wise dependence.

Keywords: Extreme value; Self-similarity; Gaussian processes; Fractional Brownian motion; Triangular arrays; Pickands constant; Piterbarg constant.; Primary 60G15; secondary 60G70 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11134-023-09880-0

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