Estimation of stationary probability of semi-Markov Chains

Nikolaos Limnios () and Bei Wu
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Nikolaos Limnios: Université de Technologie de Compiègne, Sorbonne University Alliance
Bei Wu: Beijing Institute of Technology

Statistical Inference for Stochastic Processes, 2022, vol. 25, issue 2, No 6, 355-364

Abstract: 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.

Keywords: Semi-Markov chain; Stationary probability; Estimation; Consistency; Asymptotic normality; Law of iterated logarithm; Rate of convergence; 60K15; 60J20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11203-021-09255-3

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