Article ID Journal Published Year Pages File Type
5774690 Journal of Mathematical Analysis and Applications 2018 23 Pages PDF
Abstract
This contribution is concerned with Gumbel limiting results for supremum Mn=supt∈[0,Tn]⁡|Xn(t)| with Xn,n∈N2 centered Gaussian random fields with continuous trajectories. We show first the convergence of a related point process to a Poisson point process thereby extending previous results obtained in [8] for Gaussian processes. Furthermore, we derive Gumbel limit results for Mn as n→∞ and show a second-order approximation for E{Mnp}1/p for any p≥1.
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Physical Sciences and Engineering Mathematics Analysis
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