Some Classes of Point Processes

Abstract

We dene four classes of point processes which we call A, B, *A, *B. Although we study point processes on R; these classes are suitable for generalizations for point processes on Rm and other measure metric spaces. The main result is the equivalence of classes *A and *B for point processes on R: As a matter of fact, we prove that A B A = B S; where S is the class of simple processes. We also relate these classes and the class of Poisson processes.