Continuous Time Markov Chains

Sidney I. Resnick
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Sidney I. Resnick: Cornell University, School of Operations Research and Industrial Engineering

Chapter Chapter 5 in Adventures in Stochastic Processes, 2002, pp 367-481 from Springer

Abstract: 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.

Keywords: Markov Chain; Service Time; Stationary Distribution; Poisson Process; Generator Matrix (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-1-4612-0387-2_5

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