Birth—death processes

Abstract

In the preceding chapter, we saw birth-death processes as a special class of continuous-time Markov chains. Let &#x007X(t)} denote a birth-death process. In Example 4.4, X(t) represents the size of a population at time t. A ‘birth’ increases the size by 1 and a ‘death’ decreases it by 1. However, this is indeed a rich and important class in modeling a variety of phenomena not only in biology but also in, e.g., operations research, demography, economics and engineering. Typical examples of problems that can be formulated as birth-death processes are the following.