Poisson process approximation for dependent superposition of point processes

DOI10.3150/10-BEJ290zbMath1248.60054arXiv0901.2445OpenAlexW3104681144MaRDI QIDQ453285

Aihua Xia, Louis H. Y. Chen

Publication date: 19 September 2012

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.2445

zbMATH Keywords

Stein's methodrenewal processesPoisson process approximationdependent superposition of point processessparse point processesthinned point processes

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Renewal theory (60K05)

Related Items (4)

A functional approximation for the M/G/1/N queue ⋮ A large sample property in approximating the superposition of i.i.d. finite point processes ⋮ Normal approximation for fire incident simulation using permanental Cox processes ⋮ Normal approximation for associated point processes via Stein's method with applications to determinantal point processes

Cites Work

• Position dependent and stochastic thinning of point processes
• Zero biasing and a discrete central limit theorem
• Stein's method and point process approximation
• An introduction to the theory of point processes
• A martingale approach to the Poisson convergence of simple point processes
• Distance estimates for Poisson process approximations of dependent thinnings
• Removing logarithms from Poisson process error bounds.
• Normal approximation under local dependence.
• Stein's method, Palm theory and Poisson process approximation.
• Distance estimates for dependent superpositions of point processes
• Thinning of Cluster Processes: Convergence of Sums of Thinned Point Processes
• Überlagerung verdünnter und schwach abhängiger Punktprozesse
• Limits of compound and thinned point processes
• Schwache Konvergenz von unabhängigen Überlagerungen verdünnter zufälliger Punktfolgen
• Poisson approximation for some statistics based on exchangeable trials
• Multivariate normal approximations by Stein's method and size bias couplings
• On metrics in point process approximation
• Normal approximation for random sums
• Stochastic Point Processes: Limit Theorems
• On the weak convergence of superpositions of point processes
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Poisson process approximation for dependent superposition of point processes