Multivariate second order Poincaré inequalities for Poisson functionals

DOI10.1214/19-EJP386zbMath1430.60030arXiv1803.11059MaRDI QIDQ2279325

Matthias Schulte, Joseph E. Yukich

Publication date: 12 December 2019

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

Full work available at URL: https://arxiv.org/abs/1803.11059

zbMATH Keywords

smoothingMalliavin calculusStein's methodPoisson processmultivariate normal approximationsecond order Poincaré inequality

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (13)

Multivariate approximation in total variation using local dependence ⋮ Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes ⋮ Rates of multivariate normal approximation for statistics in geometric probability ⋮ Nearly optimal central limit theorem and bootstrap approximations in high dimensions ⋮ Vector-valued statistics of binomial processes: Berry-Esseen bounds in the convex distance ⋮ Unnamed Item ⋮ Multivariate central limit theorems for random simplicial complexes ⋮ Malliavin-Stein method: a survey of some recent developments ⋮ Multivariate second order Poincaré inequalities for Poisson functionals ⋮ Multivariate normal approximation for functionals of random polytopes ⋮ Multi-dimensional normal approximation of heavy-tailed moving averages ⋮ Multivariate normal approximation on the Wiener space: new bounds in the convex distance ⋮ Quantitative two-scale stabilization on the Poisson space

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