A Central Limit Theorem for Non-Stationary Strongly Mixing Random Fields

TL;DR

This paper extends a central limit theorem to non-stationary, strongly mixing random fields, demonstrating their asymptotic normality under certain dependence and mixing conditions.

Contribution

It generalizes existing CLT results to non-stationary random fields with strong mixing and dependence conditions, without requiring stationarity.

Findings

Proves asymptotic normality of partial sums for non-stationary random fields.

Establishes CLT under Lindeberg and maximal correlation conditions.

Extends classical CLT results to broader classes of random fields.

Abstract

In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the partial sums of uniformly $\alpha$-mixing non-stationary random fields satisfying the Lindeberg condition, in the presence of an extra dependence assumption involving maximal correlations.