Estimation for Discrete-time Semi-Markov Reward Processes: Analysis and Inference

K. Khorshidian (), F. Negahdari and H. A. Mardnifard
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K. Khorshidian: Shiraz University
F. Negahdari: Shiraz University
H. A. Mardnifard: Yasouj University

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 3, 885-900

Abstract: Abstract In this paper, the moments of a class of reward processes defined on a discrete-time semi-Markov process and the asymptotic behaviors of the corresponding empirical estimators have been investigated. Some known results concerning the asymptotic distribution and properties of semi-Markov kernel have been obtained by a different approach. By using the empirical estimator of the semi-Markov kernel and the mentioned approach, the estimators for the moments of the reward process have been introduced and their asymptotic properties have been established. As a consequence of the strong consistency and asymptotic normality, the confidence intervals have also been obtained. A numerical example illustrates the results.

Keywords: Discrete-time semi-Markov processes; Reward process; Empirical estimator; Delta method; Asymptotic properties; 60K15; 62K20; 60J0 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11009-015-9468-1

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