Moments and Central Limit Theorems for Some Multivariate Poisson Functionals

Central Limit Theorems for Poisson Hyperplane

We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in Rd . This result generalizes an earlier one proved by Paroux [Adv. in Appl. Probab. 30 (1998) 640–656] for intersection points of motion-invariant Poisson line processes in R2. Our proof is based on Hoeffding’s decomposition of U -statistics which seems to be mo...

Central limit theorems for double Poisson integrals

Motivated by second order asymptotic results, we characterize the convergence in law of double integrals, with respect to Poisson random measures, toward a standard Gaussian distribution. Our conditions are expressed in terms of contractions of the kernels. To prove our main results, we use the theory of stable convergence of generalized stochastic integrals developed by Peccati and Taqqu. One ...

Central Limit Theorems for Non-Linear Functionals of Gaussian Fields

In the present paper it is shown that the central limit theorem holds for some non-linear functionals of stationary Gaussian fields if the correlation function of the underlying field tends fast enough to zero. The results are formulated in terms of the Hermite rank of the functional and of the rate of the correlation function. Then we show an example when the limit field is self-similar and Ga...

Central Limit Theorems For Dependent, Heterogeneous Processes With Trending Moments

Central Limit Theorems for Some Graphs in Computational Geometry

Let Bn be an increasing sequence of regions in d-dimensional space with volume n and with union d. We prove a general central limit theorem for functionals of point sets, obtained either by restricting a homogeneous Poisson process to Bn, or by by taking n uniformly distributed points in Bn. The sets Bn could be all cubes but a more general class of regions Bn is considered. Using this general ...