# Continuous-time Markov chain

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In probability theory, a **continuous-time Markov chain** is a mathematical model which takes values in some finite state space and for which the time spent in each state takes non-negative real values and has an exponential distribution.

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## Quotes[edit]

- 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.
- William J. Anderson (6 December 2012).
*Continuous-Time Markov Chains: An Applications-Oriented Approach*. Springer Science & Business Media. p. 8. ISBN 978-1-4612-3038-0.

- William J. Anderson (6 December 2012).