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Remark to the paper ”On some limit properties of the reward from a Markov replacement process”. (English) Zbl 0586.60045

In an earlier paper [ibid. 76, Math. 22, 143-156 (1983; Zbl 0542.60089)] the author proved two limit theorems for the rewards in a Markov replacement process, which deal with the convergence of \(t^{-1}R_ t\) to \(\Theta\) as \(t\to \infty\), where \(R_ t\) is the reward up to time t and \(\Theta\) is the mean reward per unit of time, and with the asymptotic normality of \(t^{-1/2}(R_ t-\Theta t)\). The present paper widens the scope of these theorems by weakening the assumption made initially that the replacement policy has a bounded intensity.
Reviewer: F.Papangelou

MSC:

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60K10 Applications of renewal theory (reliability, demand theory, etc.)

Citations:

Zbl 0542.60089
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References:

[1] Kunderová P.: On some limit properties of the reward from a Markov replacement process. Acta Univers. Pal. Olomucensis, F. R. N., 1983, Tom 76. · Zbl 0542.60089
[2] Liptser R. S., Shiryayev A. N.: Statistics of Random Processes II, Applications. New York, Springer Verlag, 1978. · Zbl 0369.60001
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