Abstract
In this paper, we prove the almost sure convergences for the maximum and minimum of nonstationary and stationary standardized normal vector sequences under some suitable conditions.
Highlights
The extreme phenomena in nature and human society can be explored by the classical extreme value theory [1,2,3]
The purpose of this paper is to extend the result of the almost sure central limit theorem (ASCLT) for the maximum and minimum to multivariate general normal vector sequences, which include the two cases of nonstationary and stationary, under some suitable conditions
The almost sure central limit theorems for the maxima and minimum of general normal vector n
Summary
The extreme phenomena in nature and human society can be explored by the classical extreme value theory [1,2,3]. Csáki and Gondigdanzan investigate the ASCLT for the maximum of a stationary weakly dependent Gaussian sequences [12]. Chen and Lin extend the ASCLT to nonstationary Gaussian sequences [13]. Chen et al provide an ASCLT for the maxima of multivariate stationary Gaussian sequences under some mild conditions [14]. Zhao et al explore the ASCLT for the maxima and sum of a nonstationary Gaussian vector sequence [15]. Weng et al put forward an ASCLT for the maxima and minima of a strongly dependent stationary Gaussian vector sequence [16]. The purpose of this paper is to extend the result of the ASCLT for the maximum and minimum to multivariate general normal vector sequences, which include the two cases of nonstationary and stationary, under some suitable conditions.
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