Abstract

Publisher Summary This chapter focuses on the continuous-time analog probability models of the Markov chains that have a wide variety of applications in the real world. The Poisson process is a continuous-time Markov chain having states 0, 1, 2, … and always proceeds from state n to state n + 1, where n ≥ 0. A continuous-time Markov chain is a stochastic process that moves from state to state in accordance with a discrete-time Markov chain, but is such that the amount of time it spends in each state, before proceeding to the next state, is exponentially distributed. In addition, the amount of time the process spends in state i and the next state visited must be independent random variables.

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