Conditionally independent increment point processes

Abstract

In this paper we introduce conditionally independent increment point processes, that is, processes that are conditionally independent inside and outside a bounded set A given N(A), the number of points in A. We show that these point processes can be characterized by means of the avoidance function of a multinomial `support process', the solution of a suitably defined linear system of equations, and, finally, the infinitesimal matrix of a continuous-time Markov chain.