2 - Continuous-Time Markov Chains
Published online by Cambridge University Press: 26 June 2026
Summary
This chapter treats the basic theory of continuous-time Markov processes with countable state space. After recalling (without proof) the standard textbook theory for finite state spaces, three constructions on infinite spaces are discussed in detail: the construction via the embedded Markov chain, the generator construction, and Poisson constructions. It is shown how Lyapunov functions can be used to prove that a continuous-time Markov chain is nonexplosive. This is applied together with the Poisson construction to construct some interacting particle systems for finite initial conditions only, preparing for the general existence and uniqueness results of Chapter 4.
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- A Course in Interacting Particle Systems , pp. 22 - 51Publisher: Cambridge University PressPrint publication year: 2026
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