Strong approximation of partial sums under dependence conditions with application to dynamical systems

TL;DR

This paper establishes precise convergence rates for the strong invariance principle in stationary dependent sequences, with applications to dynamical systems like intermittent maps.

Contribution

It provides new rates of convergence under weak dependence conditions, extending the strong invariance principle to broader classes of dependent sequences.

Findings

Derived explicit convergence rates for dependent sequences

Applied results to unbounded functions of intermittent maps

Extended invariance principles to weak dependence scenarios

Abstract

In this paper, we obtain precise rates of convergence in the strong invariance principle for stationary sequences of real-valued random variables satisfying weak dependence conditions including strong mixing in the sense of Rosenblatt (1956) as a special case. Applications to unbounded functions of intermittent maps are given.