Semi-Markov Process
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High Quality Content by WIKIPEDIA articles! A continuous-time stochastic process is called a semi-Markov process or 'Markov renewal process' if the embedded jump chain (the discrete process registering what values the process takes) is a Markov Chain, and where the holding times (time between jumps) are random variables with any distribution, whose distribution function may depend on the two states between which the move is made. A semi-Markov process where all the holding times are exponentially distributed is called a continuous time Markov chain/process (CTMC).

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High Quality Content by WIKIPEDIA articles! A continuous-time stochastic process is called a semi-Markov process or 'Markov renewal process' if the embedded jump chain (the discrete process registering what values the process takes) is a Markov Chain, and where the holding times (time between jumps) are random variables with any distribution, whose distribution function may depend on the two states between which the move is made. A semi-Markov process where all the holding times are exponentially distributed is called a continuous time Markov chain/process (CTMC).