Approximation of maximum of Gaussian random fields

作者：Hashorva, Enkelejd; Seleznjev, Oleg; Tan, Zhongquan^*

来源：Journal of Mathematical Analysis and Applications, 2018, 457(1): 841-867.

DOI：10.1016/j.jmaa.2017.08.040

• Maxima
• Homogeneous Gaussian random fields
• Non-homogeneous Gaussian random fields
• Pickands constant
• Piterbarg constant
• Gumbel limit theorem

This contribution is concerned with Gumbel limiting results for supremum M-n = sup(t epsilon[0,Tn])X(n)(t)vertical bar with X (n) ,n epsilon N-2 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 M-n as n -> infinity and show a second-order approximation for E{M-n(p)}(1/p) for any p >= 1.

• 出版日期2018-1-1
• 单位嘉兴学院