Resumen de Independence of thinned processes characterizes the Poisson process: An elementary proof and a statistical application

R. M. Assunção, Pablo A. Ferrari

• Let N, N 1 and N 2 be point processes such that N 1 is obtained from N by homogeneous independent thinning and N 2=N−N 1. We give a new elementary proof that N 1 and N 2 are independent if and only if N is a Poisson point process. We also present an application of this result to test if a homogeneous point process is a Poisson point process.