Continuous-time Markov chain

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A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential random variable and then move to a different state as specified by the probabilities of a stochastic matrix. An equivalent formulation describes the process as changing state according to the least value of a set of exponential random variables, one for each possible state it can move to, with the parameters determined by the current state. An example of a CTMC with three states { 0 , 1 , 2 } {\displaystyle \{0,1,2\}} is as follows: the process makes a transition after the amount of time specified by the holding time—an exponential random variable E i {\displaystyle E_{i}} , where i is its current state. Each random variable is independent and such...

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