Normal approximation of Poisson functionals in Kolmogorov distance

DOI10.1007/s10959-014-0576-6zbMath1335.60027arXiv1206.3967OpenAlexW2028534697WikidataQ101138486 ScholiaQ101138486MaRDI QIDQ270201

Matthias Schulte

Publication date: 7 April 2016

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.3967

zbMATH Keywords

Malliavin calculusStein's methodcentral limit theoremPoisson point process\(U\)-statisticsWiener-Itō chaos expansion

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stochastic calculus of variations and the Malliavin calculus (60H07) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

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Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences, Classical and free fourth moment theorems: universality and thresholds, The fourth moment theorem on the Poisson space, Does a central limit theorem hold for the \(k\)-skeleton of Poisson hyperplanes in hyperbolic space?, The Malliavin–Stein Method on the Poisson Space, U-Statistics in Stochastic Geometry, Poisson Point Process Convergence and Extreme Values in Stochastic Geometry, Intersections of Poisson \(k\)-flats in constant curvature spaces, Normal approximation in total variation for statistics in geometric probability, Convergence rate for geometric statistics of point processes having fast decay of dependence, Unnamed Item, Multivariate central limit theorems for random simplicial complexes, Distances between Poisson \(k\)-flats, Normal approximation for stabilizing functionals, Fourth moment theorems on the Poisson space in any dimension, Multivariate second order Poincaré inequalities for Poisson functionals, Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization, Quantitative two-scale stabilization on the Poisson space, Limit theory for the Gilbert graph

Cites Work

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