Compound Poisson process approximation.

DOI10.1214/aop/1029867135zbMath1033.60059OpenAlexW2172154460MaRDI QIDQ1872302

Marianne Månsson, Andrew David Barbour

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1029867135

zbMATH Keywords

rare eventsmetricdistanceStein equation

Mathematics Subject Classification ID

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

Related Items (15)

Strong memoryless times and rare events in Markov renewal point processes. ⋮ Stein's method, Palm theory and Poisson process approximation. ⋮ Compound Poisson process approximation for locally dependent real-valued random variables via a new coupling inequality ⋮ A large sample property in approximating the superposition of i.i.d. finite point processes ⋮ Wasserstein distance on configuration space ⋮ On the asymptotics of locally dependent point processes ⋮ A new metric between distributions of point processes ⋮ Gibbs point process approximation: total variation bounds using Stein's method ⋮ A polynomial birth-death point process approximation to the Bernoulli process ⋮ Optimal transport between determinantal point processes and application to fast simulation ⋮ A mixture‐distribution factor model for multivariate outliers ⋮ A mixture‐distribution factor model for multivariate outliers ⋮ The Stein-Dirichlet-Malliavin method ⋮ A Compound Poisson Approximation Inequality ⋮ Distance estimates for dependent superpositions of point processes

Cites Work

• Unnamed Item
• Unnamed Item
• Two moments suffice for Poisson approximations: The Chen-Stein method
• Probability approximations via the Poisson clumping heuristic
• Stein's method and point process approximation
• Compound Poisson approximation for nonnegative random variables via Stein's method
• Compound Poisson approximation in total variation
• Compound Poisson approximation for Markov chains using Stein's method
• Stein's method and birth-death processes
• Compound Poisson approximation: A user's guide
• On Compound Poisson Approximation for Sequence Matching
• Solving the Stein Equation in compound poisson approximation
• A Phase Transition for the Distribution of Matching Blocks

This page was built for publication: Compound Poisson process approximation.