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Continuous Time Markov Chains

In: Adventures in Stochastic Processes

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  • Sidney I. Resnick

    (Cornell University, School of Operations Research and Industrial Engineering)

Abstract

WE TURN now to the continuous time version of the Markov property. Some of the simplicity of Chapter 2 is retained, because we assume the state space S is discrete. Usually we can suppose that S = {0, 1, … }. The succession of states visited still follows a discrete parameter Markov chain but now the flow of time is perturbed by exponentially distributed holding times in each state. An easy generalization of the dissection argument of Chapter 2 shows that the process regenerates at return times to a fixed reference state, so renewal theory and regenerative processes are useful.

Suggested Citation

  • Sidney I. Resnick, 2002. "Continuous Time Markov Chains," Springer Books, in: Adventures in Stochastic Processes, chapter 0, pages 367-481, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0387-2_5
    DOI: 10.1007/978-1-4612-0387-2_5
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