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

2010/11/26 by Matthias Schulte, Schulte, Matthias, Christoph Thaele +1 · 1 citation
Mathematics · Economics, Econometrics and Finance · #Point processes and geometric inequalities #Stochastic processes and statistical mechanics #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1011.5777

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.

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• The Chen-Stein method for Poisson functionals

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