Options
Poisson process approximation under stabilization and palm coupling
Citation Link: https://doi.org/10.15480/882.15798
Other Titles
Approximation par processus de poisson sous stabilisation et couplage de palm
Publikationstyp
Journal Article
Date Issued
2022-01-01
Sprache
English
TORE-DOI
Journal
Volume
5
Start Page
1489
End Page
1534
Citation
Annales Henri Lebesgue 5: 1489-1534 (2022)
Publisher DOI
Scopus ID
Publisher
École Normale Supérieure de Rennes
We present new Poisson process approximation results for stabilizing functionals of Poisson and binomial point processes. These functionals are allowed to have an unbounded range of interaction and encompass many examples in stochastic geometry. Our bounds are derived for the Kantorovich–Rubinstein distance using the generator approach to Stein’s method. We give different types of bounds for different point processes. While some of our bounds are given in terms of coupling of the point process with its Palm version, the others are in terms of the local dependence structure formalized via the notion of stabilization. We provide two supporting examples for our new framework– one is for Morse critical points of the distance function, and the other is for large k-nearest neighbor balls. Our bounds considerably extend the results in Barbour and Brown (1992), Decreusefond, Schulte and Thäle (2016) and Otto (2020).
Subjects
Binomial point processes | Functional limit theorems | Glauber dynamics | k-nearest neighbor balls | Kantorovich-Rubinstein distance | Morse critical points | Palm coupling | Point processes | Poisson process approximation | Stabilizing statistics | Stein’s method
DDC Class
519: Applied Mathematics, Probabilities
Publication version
publishedVersion
Loading...
Name
AHL_2022__5__1489_0.pdf
Type
Main Article
Size
787.43 KB
Format
Adobe PDF