Rates of convergence in the strong invariance principle under projective criteria

TL;DR

This paper establishes convergence rates in the strong invariance principle for stationary sequences under projective criteria, applicable to various dependent processes including mixing sequences and Markov chains.

Contribution

It introduces new convergence rate results based on projective criteria, extending the applicability to diverse dependent sequences and processes.

Findings

Convergence rates are derived for stationary sequences under projective conditions.

Results apply to mixing processes, symmetric random walks, and reversible Markov chains.

The paper demonstrates practical applications to dependent sequences and stochastic processes.

Abstract

We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our results apply to a large variety of examples, including mixing processes of different kinds. We present some applications to symmetric random walks on the circle, to functions of dependent sequences, and to a reversible Markov chain.