Negative binomial distributions for point processes

Abstract

Negative binomial point processes are defined for which all finite-dimensional distributions associated with disjoint bounded Borel sets are negative binomial in the usual sense. For these processes we study classical notions such as infinite divisibility, conditional distributions, Palm probabilities, convergence, etc. Negative binomial point processes appear to be of interest because they are mathematically tractable models which can be used in many situations. The general results throw some new light on some well-known special cases like the Polya process and the Yule process.