Cet article traite du processus ponctuel d’intersection d’un d’hyperplans de Poisson stationnaire et isotrope dans Rd d’intensité t>0, où seuls les hyperplans qui intersectent une boule centrée rayon R>0 sont considérés. En prenant R=t−dd+1, on montre que ce converge en distribution, lorsque t→∞, vers un Rd∖{0} dont la mesure a densité proportionnelle à ‖x‖−(d+1) par rapport Lebesgue. Une borne...

Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and tractability. However, this assumption seems be restrictive when dealing counting data. To deal situation, we propose a Poisson marginal distribution considering sequ...

This paper analyzes statistical properties of the Poisson line Cox point process useful in the modeling of vehicular networks. The point process is created by a two-stage construction: a Poisson line process to model road infrastructure and independent Poisson point processes, conditionally on the Poisson lines, to model vehicles on the roads. We derive basic properties of the point process, in...

We present sufficient conditions for sums of dependent point processes to converge in distribution to a Poisson process. This extends the classical result of Grigelionis [Theory Probab. Appl. 8 (1963) 172– 182] for sums of uniformly null point processes that have Poisson limits. Included is an application in which a particle-survivor point process converges to a Poisson process. This result she...

Let N , N1 and N2 be point processes such that N1 is obtained from N by homogeneous independent thinning and N2 = N −N1. We give a new elementary proof that N1 and N2 are independent if and only if N is a Poisson point process. We present some applications of this result to test if a homogeneous point process is a Poisson point process.

Let P1 be a Poisson process of intensity λ1 on the positive x-axis, P2 a Poisson process of intensity λ2 on the positive y-axis, and P a Poisson process of intensity λ1λ2 in the interior of IR +, where P1, P2 and P are independent. Then the extended Hammersley process Lλ1(·, t) with sources and sinks given by P1 and P2, respectively, is distributed as a Poisson point process with intensity λ1 f...