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Functions of Semi-Markov Processes
SIAM Journal on Applied Mathematics, 1971A necessary and sufficient condition is presented under which a function of a semi-Markov process is again a semi-Markov process with transition probabilities which do not depend on the initial distribution of the original process. This result is a generalization of a known result for Markov processes.
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Continuity of Generalized Semi-Markov Processes
Mathematics of Operations Research, 1980It is shown that sequences of generalized semi-Markov processes converge in the sense of weak convergence of random functions if associated sequences of defining elements (initial distributions, transition functions and clock time distributions) converge.
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2001
Let Q(x,A,t), x ∈ E, A ∈ e,t ∈ IR+, be a semi-Markov kernel on (E,e) and let (J n ,S n )n∈N and (J n ,X n )n∈N be, respectively, the associated MRP and the (J-X)-process (see Section 2.2).
N. Limnios, G. Oprişan
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Let Q(x,A,t), x ∈ E, A ∈ e,t ∈ IR+, be a semi-Markov kernel on (E,e) and let (J n ,S n )n∈N and (J n ,X n )n∈N be, respectively, the associated MRP and the (J-X)-process (see Section 2.2).
N. Limnios, G. Oprişan
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Regenerative generalized semi-markov processes
Communications in Statistics. Stochastic Models, 1987The authors deal with a generalized semi-Markov process, which permits formal specification of some non-Markovian simulation models.
Haas, Peter J., Shedler, Gerald S.
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On Integral of a Semi-Markov Diffusion Process
Journal of Mathematical Sciences, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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SEMI-MARKOV DECISION PROCESSES
Probability in the Engineering and Informational Sciences, 2007Considered are semi-Markov decision processes (SMDPs) with finite state and action spaces. We study two criteria: the expected average reward per unit time subject to a sample path constraint on the average cost per unit time and the expected time-average variability.
M. Baykal-Gürsoy, K. Gürsoy
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Semi-Markov failure rates processes
Applied Mathematics and Computation, 2011Let \(\{\lambda(u):u\geq 0\}\) be a semi-Markov process defined by a Markov renewal kernel. The author studies the survival function \(R\) defined as the expectation of \(\exp \left(-\int_0^t\lambda(u)du\right)\), for \(t \geq 0\). Note that, \(R(t)\) is considered to be the reliability of an object with a random failure rate.
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Semi-Markov Model of Damage Process
2016Semi-Markov model of an object damage process is discussed in the paper. Presented here models deal with unrepairable object. The multi-state reliability functions and corresponding expectations, second moments and standard deviations are evaluated for the presented cases of the object damage.
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On the entropy for semi-Markov processes
Journal of Applied Probability, 2003The aim of this paper is to define the entropy of a finite semi-Markov process. We define the entropy of the finite distributions of the process, and obtain explicitly its entropy rate by extending the Shannon–McMillan–Breiman theorem to this class of nonstationary continuous-time processes.
Girardin, Valerie, Limnios, Nikolaos
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