Markov-bridge representation of ergodic large-deviation principles

TL;DR

This paper introduces a new Markov-bridge framework for ergodic large-deviation principles, providing alternative expressions for rate functionals related to occupation measures and empirical fluxes.

Contribution

It embeds classic ergodic large-deviation principles into a discrete-time Markov-bridge framework, offering novel formulations and insights.

Findings

Derived alternative expressions for rate functionals

Unified treatment of occupation measure and empirical flux

Enhanced understanding of large deviations via Markov bridges

Abstract

We revisit classic ergodic large-deviation principles: for the occupation measure (Donsker-Varadhan), and for the empirical flux. We show that these problems can be embedded into a more general, discrete-time framework. A conditioning and mixing argument then yields alternative expressions for these well-known rate functionals, formulated in terms of Markov bridges.