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Estimation of stationary probability of semi-Markov Chains

Author

Listed:
  • Nikolaos Limnios

    (Université de Technologie de Compiègne, Sorbonne University Alliance)

  • Bei Wu

    (Beijing Institute of Technology)

Abstract

This paper concerns the estimation of stationary probability of ergodic semi-Markov chains based on an observation over a time interval. We derive asymptotic properties of the proposed estimator, when the time of observation goes to infinity, as consistency, asymptotic normality, law of iterated logarithm and rate of convergence in a functional setting. The proofs are based on asymptotic results on discrete-time semi-Markov random evolutions.

Suggested Citation

  • Nikolaos Limnios & Bei Wu, 2022. "Estimation of stationary probability of semi-Markov Chains," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 355-364, July.
    • Handle: RePEc:spr:sistpr:v:25:y:2022:i:2:d:10.1007_s11203-021-09255-3
    DOI: 10.1007/s11203-021-09255-3
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    References listed on IDEAS

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    1. Limnios, N., 2006. "Estimation of the stationary distribution of semi-Markov processes with Borel state space," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1536-1542, August.
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