Generalities

Abstracts

This chapter introduces the notions of random measure, point process with or without marks, intensity measure and stochastic integral with respect to a point process. It gives the main avatars of the celebrated Campbell formula and the distribution theory of point processes (Laplace functional, avoidance probability) together with the basic notions and some elementary results concerning the convergence in distribution or in variation of random measures. It also features important classes of point processes: the Poisson process, the Cox process and the cluster point processes, whose study will be continued in the subsequent chapters. A summary of the Stieltjes–Lebesgue calculus, which is especially relevant to the study of stochastic systems driven by point processes, is included in this preliminary chapter.