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Markov Chains by J. R. Norris

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2Continuous-time Markov chains I

The material on continuous-time Markov chains is divided between this chapter and the next. The theory takes some time to set up, but once up and running it follows a very similar pattern to the discrete-time case. To emphasise this we have put the setting-up in this chapter and the rest in the next. If you wish, you can begin with Chapter 3, provided you take certain basic properties on trust, which are reviewed in Section 3.1. The first three sections of Chapter 2 fill in some necessary background information and are independent of each other. Section 2.4 on the Poisson process and Section 2.5 on birth processes provide a gentle warm-up for general continuous-time Markov chains. These processes are simple and ...

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