Exact and asymptotic results for intrinsic volumes of Poisson k-flat processes

Abstract

The intrinsic volumes induced by a stationary Poisson k-flat process inside a compact and convex sampling window are considered. Using techniques from stochastic analysis, more precisely calculus with multiple stochastic integrals and a Wiener-Ito chaos expansion of Poisson functionals, all moments and cumulants, exact and asymptotic, are calculated in terms of a family of integral-geometric functionals. Moreover, univariate central limit theorems as well as Berry-Esseen-type inequalities are shown and a multidimensional limit theorem is concluded.

References in corpus (1)

• Central limit theorems for Poisson hyperplane tessellations

Cited by in corpus (4)

• Central limit theorems for $U$-statistics of Poisson point processes
• The Chen-Stein method for Poisson functionals
• Fine Gaussian fluctuations on the Poisson space II: rescaled kernels, marked processes and geometric U-statistics
• Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering