Poisson-sampled continuous-time Markov chain ($P_{\lambda }=\lambda (\lambda I-Q{)}^{-1}$)

Sample a finite-state continuous-time Markov chain with generator $Q$ at the independent arrival times of a rate-$\lambda$ Poisson process. The sampled states form a discrete-time Markov chain with transition matrixIts invariant distributions are exactly those of the continuous-time chain.