Poisson Processes as Particular Markov Processes.

Summary We first introduce some practical and theoretical issues of modeling by means of Markov processes. Point processes are introduced in order to model jump instants. The Poisson process is then characterized as a point process without memory. The rest of the chapter consists in its rather detailed study, including various results concerning its simulation and approximation. This study is essential to understand the abstract constructions and the simulation methods for jump Markov processes developed in the following chapters.