An alternative to the coupling of Berkes-Liu-Wu for strong approximations

TL;DR

This paper introduces a new coupling method using a Rosen-thal type inequality to achieve strong approximations for dependent sequences, improving applicability to Markov chains, dynamical systems, and smooth functions of linear processes.

Contribution

It presents an alternative coupling approach with a novel inequality, expanding the tools for strong approximation of dependent sequences.

Findings

Effective coupling method for Markov chains and dynamical systems.

New results for smooth functions of linear processes.

Enhanced strong approximation techniques for dependent data.

Abstract

In this paper we propose an alternative to the coupling of Berkes, Liu and Wu [1] to obtain strong approximations for partial sums of dependent sequences. The main tool is a new Rosen-thal type inequality expressed in terms of the coupling coefficients. These coefficients are well suited to some classes of Markov chains or dynamical systems, but they also give new results for smooth functions of linear processes.