Edgeworth expansions in operator form

TL;DR

This paper develops an operator-based approach to asymptotic expansions for Markov chains, providing explicit coefficients and modifications to classical spectral methods, with significant applications in large deviations analysis.

Contribution

Introduces an operator form of asymptotic expansions for Markov chains with explicit coefficients and a modified spectral method, enhancing large deviations analysis.

Findings

Established an operator form of asymptotic expansions for Markov chains

Provided explicit formulas for the coefficients in the expansions

Demonstrated usefulness in large deviations contexts

Abstract

An operator form of asymptotic expansions for Markov chains is established. Coefficients are given explicitly. Such expansions require a certain modification of the classical spectral method. They prove to be extremely useful within the context of large deviations.