Approximation of maximum of Gaussian random fields

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.