Continuous Time Modeling for Birth and Death Processes

Abstract

In this chapter, we shall describe the fundamental modeling with the birth-death stochastic process. The idea and concept in such a modeling is very important to understand the meaning of modeling about the deterministic mathematical model which superficially seems not to have any relation to the stochasticity in the phenomenon. In almost all modeling for the population dynamics, the deterministic model could be actually regarded as an approximation to describe an important aspect about the phenomenon. To understand the reasonability of the deterministic structure introduced in the model, it is necessary and useful to know its relation to a stochastic process. For this reason, this chapter contains the idea and concept essential throughout the contents in this book. As the simplest and most important stochastic process, the Poisson process is introduced and used in some parts of this book. Chapter 15 of Part II serves to provide the mathematical fundamentals about it.