Continuous-time Markov Process

In probability theory, a continuous-time Markov process is a stochastic process { X(t) : t ≥ 0 } that satisfies the Markov property and takes values from a set called the state space; it is the continuous-time version of a Markov chain. The Markov property states that at any times s > t > 0, the conditional probability distribution of the process at time s given the whole history of the process up to and including time t, depends only on the state of the process at time t. In effect, the state of the process at time s is conditionally independent of the history of the process before time t, given the state of the process at time t. In simple terms the process can be thought of as memory-less.

Read more about Continuous-time Markov Process:  Mathematical Definitions, Embedded Markov Chain, Applications

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Continuous-time Markov Process - Applications - Queueing Theory
... Then the number of jobs in the queue is a continuous time Markov process on the non-negative integers ...

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