Moderate deviations for stationary sequences of bounded random variables

TL;DR

This paper establishes the moderate deviation principle for stationary bounded sequences under martingale conditions, with applications to various stochastic processes including mixing sequences, Markov chains, and random walks.

Contribution

It introduces the moderate deviation principle for stationary bounded sequences under martingale-type conditions, extending its applicability to multiple classes of stochastic processes.

Findings

Moderate deviation principle derived for stationary sequences.

Applications demonstrated for mixing sequences, Markov chains, and random walks.

Provides theoretical foundation for analyzing deviations in bounded stochastic processes.

Abstract

In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of $\phi$-mixing sequences, contracting Markov chains, expanding maps of the interval, and symmetric random walks on the circle are given.