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High Quality Content by WIKIPEDIA articles! A semi-Markov process is a process that changes states according to a discrete time Markov Chain but stays at each state for a random amount of time with distribution Hn. A Continuous Time Markov Chain is a special case of a semi-Markov process in which the transition times are exponentially distributed with rate . A Markov process, named after the Russian mathematician Andrey Markov, is a mathematical model for the random evolution of a memoryless system, that is, one for which the likelihood of a given future state, at any given moment, depends only on its present state, and not on any past states. In a common description, a stochastic process with the Markov property, or memorylessness, is one for which conditional on the present state of the system, its future and past are independent.