Quasi-ergodic limits for finite absorbing Markov chains

TL;DR

This paper derives formulas for quasi-ergodic limits in finite reducible absorbing Markov chains, extending classical results to cases with complex path growth behaviors through detailed asymptotic analysis.

Contribution

It provides new formulas for quasi-ergodic limits in reducible chains, building on prior work that focused on irreducible cases, with a focus on asymptotic path analysis.

Findings

Formulas for quasi-ergodic limits in reducible chains

Asymptotic analysis of exponential and polynomial growth

Extension of classical results to more complex chain structures

Abstract

We present formulas for quasi-ergodic limits of finite absorbing Markov chains. Since the irreducible case has been solved in 1965 by Darroch and Seneta, we focus on the reducible case, and our results are based on a very precise asymptotic analysis of the (exponential and polynomial) growth behaviour along admissible paths