Continuous-time Markov chain

Summary

A continuous-time Markov chain is a process with values in a countable set that jumps between states at random times and has the Markov property. It stays in each state for an exponentially distributed time, and then jumps according to fixed probabilities. Its law is described by a rate matrix $Q$, and on a finite set its transition probabilities form the matrix exponential $e^{tQ}$. Queues, birth–death processes and the Poisson process are standard examples.