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An identity for the bias in Markov reward processes with applications to Markov chain perturbation and Kemeny’s constant

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  • Ortner, Ronald

Abstract

Given a unichain Markov reward process (MRP), we provide an explicit expression for the bias values in terms of mean first passage times. This result implies a generalization of known Markov chain perturbation bounds for the stationary distribution to the case where the perturbed chain is not irreducible. It further yields an improved perturbation bound in 1-norm. As a special case, Kemeny’s constant can be interpreted as the translated bias in an MRP with constant reward −1, which offers an intuitive explanation why it is a constant.

Suggested Citation

  • Ortner, Ronald, 2026. "An identity for the bias in Markov reward processes with applications to Markov chain perturbation and Kemeny’s constant," Statistics & Probability Letters, Elsevier, vol. 230(C).
    • Handle: RePEc:eee:stapro:v:230:y:2026:i:c:s0167715225002378
    DOI: 10.1016/j.spl.2025.110592
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