Continuous-time Markov chain

In probability theory, a continuous-time Markov chain (CTMC or continuous-time Markov process) 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. It is a continuous-time stochastic process with the Markov property which means that future behaviour of the model (both remaining time in current state and next state) depends only on the current state of the model and not on historical behaviour. The model is a continuous-time version of the Markov chain model, named because the output from such a process is a sequence (or chain) of states.