Stochastic point processes and multicoincidences

In this paper stochastic point processes (PP) are studied by means of coincidence probabilities (CP). After a definition and short review of these CP, it is shown that they provide a complete statistical description of the PP. All the statistics of the resulting shot noise are derived and time intervals between successive occurrences are studied and related to CP. Some new applications, including the "generalized" renewal process, illustrate the coincidence approach. The method applies very well to such cases as nonstationary or multidimensional PP.