A Central Limit Theorem For Linear Random Fields

TL;DR

This paper establishes a Central Limit Theorem for linear random fields over unions of rectangles, extending classical results and providing a uniform analogue of Ibragimov's theorem without relying on Beveridge Nelson decomposition.

Contribution

It introduces a new CLT for linear random fields over unions of rectangles, generalizing existing results with a novel approach that avoids Beveridge Nelson decomposition.

Findings

Proves a CLT for sums over disjoint unions of rectangles in linear random fields.

Provides conditions similar to Ibragimov's for linear processes, ensuring the theorem's applicability.

Achieves a uniform analogue of Ibragimov's result for rectangular sums.

Abstract

A Central Limit Theorem is proved for linear random fields when sums are taken over finite disjoint union of rectangles. The approach does not rely upon the use of Beveridge Nelson decomposition and the conditions needed are similar to those given by Ibragimov for linear processes. When specializing this result to the case when sums are being taken over rectangles, a complete analogue of Ibragimov result is obtained with a lot of uniformity.