Normal approximation for random sums

DOI10.1239/aap/1158684998zbMath1106.60029OpenAlexW2152349675MaRDI QIDQ5395356

Aihua Xia, Andrew David Barbour

Publication date: 2 November 2006

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/aap/1158684998

zbMATH Keywords

Stein's methodBerry-Esseen boundRandom fieldPoint processLocal dependenceTwo-dimensional maximum

Mathematics Subject Classification ID

Random fields (60G60) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Random measures (60G57)

Related Items (18)

Random central limit theorem for associated random variables and the order of approximation ⋮ Multivariate approximation in total variation using local dependence ⋮ Berry-Esseen Bounds for Random Index Non Linear Statistics via Stein's Method ⋮ Stochastic comparisons of multivariate random sums in the Laplace transform order, with applications ⋮ Gaussian approximation for rooted edges in a random minimal directed spanning tree ⋮ A risk model for Forest fires based on asymptotic results for multivariate collective models. Single models and structured families of models ⋮ Rates of multivariate normal approximation for statistics in geometric probability ⋮ Asymptotic results for random sums of dependent random variables ⋮ Cramér-type moderate deviation for Studentized compound Poisson sum ⋮ On the asymptotics of locally dependent point processes ⋮ Poisson process approximation for dependent superposition of point processes ⋮ Normal approximation for stabilizing functionals ⋮ Surface order scaling in stochastic geometry ⋮ Normal approximation for statistics of Gibbsian input in geometric probability ⋮ Asymptotic theory for statistics of the Poisson-Voronoi approximation ⋮ Moderate deviations for some point measures in geometric probability ⋮ Palm theory, random measures and Stein couplings ⋮ Gaussian approximation for sums of region-stabilizing scores

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