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Probability and Statistics with Reliability, Queuing, and Computer Science Applications, 2nd Edition by Kishor S. Trivedi

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Chapter 8Continuous-Time Markov Chains

8.1 Introduction

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 c08-math-0002 is discrete. Let c08-math-0003 denote the state space of the process, and c08-math-0004 be its parameter space. Recalling from Chapter 6, a discrete-state continuous-time stochastic process c08-math-0005 is called a Markov chain if for c08-math-0006, with t and c08-math-0008, 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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