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Stein’s method for ergodic rates of stochastically monotone Markov chains

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  • Zhu, Jiangle
  • Liu, Jinpeng
  • Li, Wendi

Abstract

Stein’s method is a powerful tool for quantifying the distance between probability distributions. In this note, we apply this method to study stationary distributions of stochastically monotone Markov chains. Building upon and extending the work of Daly (2024), we characterize the rate of convergence to stationarity in terms of the solution of Poisson’s equation and the expected first return time. Our results are illustrated with applications to discrete-time downward skip-free Markov chains, including birth–death chains and the embedded Markov chains of M/G/1 queues.

Suggested Citation

  • Zhu, Jiangle & Liu, Jinpeng & Li, Wendi, 2026. "Stein’s method for ergodic rates of stochastically monotone Markov chains," Statistics & Probability Letters, Elsevier, vol. 237(C).
    • Handle: RePEc:eee:stapro:v:237:y:2026:i:c:s0167715226001860
    DOI: 10.1016/j.spl.2026.110822
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