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Estimation of the stationary distribution of semi-Markov processes with Borel state space

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  • Limnios, N.

Abstract

We present an empirical estimator of the stationary distribution of continuous time semi-Markov processes with Borel state space. It comes as a particular case of an estimator of a linear functional of the stationary distribution. We give asymptotic results for strong consistency, and the weak and strong invariance principles.

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  • 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.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:14:p:1536-1542
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    References listed on IDEAS

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    1. Brahim Ouhbi & Nikolaos Limnios, 1999. "Nonparametric Estimation for Semi-Markov Processes Based on its Hazard Rate Functions," Statistical Inference for Stochastic Processes, Springer, vol. 2(2), pages 151-173, May.
    2. Krishna B. Athreya & Mukul Majumdar, 2003. "Estimating the stationary distribution of a Markov chain," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 729-742, March.
    3. Paul F. M. Krabbe & Eddy M. M. Adang & Peep F. M. Stalmeier & Bruce R. Schackman & John Brazier & Milton C. Weinstein, 2003. "Letter to the Editor," Medical Decision Making, , vol. 23(6), pages 542-543, November.
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    1. 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.

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