# Continuous Time Markov Chains

What are some techniques to convert Continuous Time Markov Processes into Discrete time Markov Processes? (for purposes of simulations)

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Fix $h>0$ and consider $\xi_n=X_{nh}$ for every integer $n\ge0$. If $(X_t)$ is a Markov process with Q-matrix $Q$, then $(\xi_n)$ is a Markov chain with transition matrix $P=\mathrm{e}^{hQ}$. If $h$ is small one can hope to get some information on $(X_t)$ from the study of $(\xi_n)$.