Coincidence analysis of point processes

A point process can be fully described by its coincidence probabilities but the expressions giving counting and life time statistics in terms of coincidence are so complicated that they cannot be used practically. However an analysis limited to bicoincidence yields already important properties of the time behavior of point processes. In particular it explains entirely the bunching or antibunching effect of point processes. In the case of compound Poisson processes, the bicoincidence probability is a correlation function and the bunching effect is simply related to the maximum at the origin of any correlation function. However, there are many other point processes that also show antibunching. Thus the relation between coincidence and correlation must be analyzed more carefully. Similar problems appear when relating the bunching effect to some statistical properties of counting. In order to clarify the question, various examples of point processes are discussed and numerical calculations illustrate the results.