The analysis of continuous-time Markov chains (CTMCs) is similar to that of the discrete-time case, except that the transitions from a given state to another state can take place at any instant of time. As in the last chapter, we confine our attention to **discrete-state** processes. This implies that, although the parameter *t* has a continuous range of values, the set of values of is discrete. Let denote the state space of the process, and be its parameter space. Recalling from Chapter 6, a discrete-state continuous-time stochastic process is called a Markov chain if for , with *t* and , its conditional pmf satisfies the relation

The behavior of the process is characterized by (1) the initial state probability vector of the CTMC ...

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