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Semi-Markov Processes: Applications in System Reliability and Maintenance by Franciszek Grabski

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5

Stochastic processes associated with the SM process

Abstract

Random processes determined by the characteristics of the semi-Markov process are considered in this chapter. First is a renewal process generated by return times of a given state. The systems of equations for the distribution and expectation of them have been derived. The limit theorem for the process is formulated by adopting a theorem of the renewal theory. The limiting properties of the alternating process and integral functionals of the semi-Markov process are presented in this chapter. The chapter contains illustrative examples.

Keywords

Renewal process

Alternating process

Cumulative process

Integral functionals of the semi-Markov process

5.1 The renewal process generated ...

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