Definition and Examples of Continuous‐Time M arkov Chains
Evin Uzun · Wiley Encyclopedia of Operations Research and Management Science · 2011
Abstract This article consists of definitions and examples of continuous‐time Markov chains (CTMCs). We first define a CTMC as a continuous‐time stochastic process that has a countable state space and the Markov property. Then, we restrict our attention to time‐homogenous CTMCs, for which we define the transition probability matrix. We further restrict our attention to regular CTMCs and provide an alternative definition of a CTMC. Next, we define the embedded discrete‐time Markov chain and the generator matrix of a CTMC and investigate the possible ways of characterizing a CTMC. We complete the definitions by defining the transition rate diagram of a CTMC. Finally, we conclude the article by providing examples of CTMCs.