Deviation inequalities for dependent sequences with applications to strong approximations

TL;DR

This paper establishes precise convergence rates in the strong invariance principle for weakly dependent stationary sequences, introducing a new inequality and applying it to various process classes.

Contribution

It provides a novel Fuk-Nagaev type inequality for weakly dependent sequences and extends strong invariance principles to broader process classes.

Findings

Derived explicit convergence rates in strong invariance principles.

Introduced a new inequality for weakly dependent sequences.

Applied results to multiple classes of stochastic processes.

Abstract

In this paper, we give precise rates of convergence in the strong invariance principle for stationary sequences of bounded real-valued random variables satisfying weak dependence conditions. One of the main ingredients is a new Fuk-Nagaev type inequality for a class of weakly dependent sequences. We describe also several classes of processes to which our results apply.