The maxima and sums of multivariate non-stationary Gaussian sequences

Abstract

Let {X k1 , · · · , X kp , k ≥ 1} be a p-dimensional standard (zero-means, unit-variances) non-stationary Gaussian vector sequence. In this work, the joint limit distribution of the maxima of {X k1 , · · · , X kp , k ≥ 1}, the incomplete maxima of those sequences subject to random failure and the partial sums of those sequences are obtained.

On the maxima and sums of homogeneous Gaussian random fields

“…In analogy, the sequence X with correlation function satisfying condition (1) with γ > 0 is called strongly dependent Gaussian sequence. For some recent work on the joint limiting distribution of partial sums and maxima for Gaussian sequences, we refer to Tan and Yang (2015) and the references therein. In this work, we are interested in the limit theorem for the maxima and partial sums of weakly and strongly dependent Gaussian random fields.…”