Poisson approximation for point processes via monotone couplings

DOI10.1214/aoap/1034968143zbMath0865.60037OpenAlexW2058672386MaRDI QIDQ1814750

Timothy C. Brown, Darryl Greig

Publication date: 7 July 1997

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

Full work available at URL: https://doi.org/10.1214/aoap/1034968143

zbMATH Keywords

Palm measuresStein-Chen bounds for the accuracy of Poisson approximationtotal number of points in a point process

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Approximations to statistical distributions (nonasymptotic) (62E17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Renewal theory (60K05)

Related Items (2)

On using the first difference in the Stein-Chen method ⋮ A Compound Poisson Model for Word Occurrences in DNA Sequences

Cites Work

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• Palm probabilities and stationary queues
• Two moments suffice for Poisson approximations: The Chen-Stein method
• Bounds, inequalities, and monotonicity properties for some specialized renewal processes
• Point processes and queues. Martingale dynamics
• The Stein-Chen method, point processes and compensators
• Compound Poisson approximation for nonnegative random variables via Stein's method
• An introduction to the theory of point processes
• Poisson approximation for dependent trials
• Event and time averages: a review
• Approximate versions of Melamed's theorem

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