"The end of the fifties marked somewhat of a watershed for continuous time Markov chains, with two branches emerging a theoretical school following Doob and Chung, attacking the problems of continuous-time chains through their sample paths, and using measure theory, martingales, and stopping times as their main tools; and an applications oriented school following Kendall, Reuter and Karlin, studying continuous chains through the transition function, enriching the field over the past thirty years with concepts such as reversibility, ergodicity, and stochastic monotonicity inspired by real applications of continuous-time chains to queueing theory, demography, and epidemiology."
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Continuous-time Markov chain
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