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.
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The authors are grateful to the anonymous referees for their detailed remarks and suggestions which led to significant improvements in the presentation of this paper.
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Limnios, N., Wu, B. Estimation of stationary probability of semi-Markov Chains. Stat Inference Stoch Process 25, 355–364 (2022). https://doi.org/10.1007/s11203-021-09255-3
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DOI: https://doi.org/10.1007/s11203-021-09255-3
Keywords
- Semi-Markov chain
- Stationary probability
- Estimation
- Consistency
- Asymptotic normality
- Law of iterated logarithm
- Rate of convergence