If $\{X_n\}$ is a Markov chain, $N(t)$ is a poisson process. Can we say that $X_{N(t)}$ is a continuous Markov chain? How to prove that?
2026-03-25 12:54:14.1774443254
Can we combine a Markov chain and a Poisson process to construct a continuous Markov chain?
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Yes. See page 119 of Essentials of Stochastic Processes, by Rick Durrett.