September 2014
Intermediate to advanced
270 pages
8h 1m
English
Content preview from Semi-Markov Processes
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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