The central limit theorem for a sequence of random processes with space varying long memory

TL;DR

This paper proves a central limit theorem for sequences of random processes with space-varying long memory, using a non-standard normalization in the $L^2(u)$ space, under specific conditions.

Contribution

It establishes the CLT for space-varying long memory processes with a novel normalization approach in $L^2(u)$ space.

Findings

Sufficient conditions for CLT in $L^2(u)$ for such processes

Introduction of a non-standard normalization method

Extension of CLT to processes with space-varying long memory

Abstract

In this paper we investigate a sequence of square integrable random processes with space varying memory. We establish sufficient conditions for the central limit theorem in the space $L^2(\mu)$ for the partial sums of the sequence of random processes with space varying long memory. Of particular interest is a non-standard normalization of the partial sums in the central limit theorem.