Negative binomial processes

Abstract

SummaryThis paper is concerned with negative binomial processes which are essentially mixed Poisson processes whose intensity parameter is given by the sum of squares of a finite number of independently and identically distributed Gaussian processes. A study is made of the distribution of the number of points of a k-dimensional negative binomial process in a compact subset of Rk, and in particular in the case where the underlying Gaussian processes are independent Ornstein-Uhlenbeck processes when more detailed results may be obtained.