CENTRAL LIMIT THEOREMS FOR U-STATISTICS OF POISSON POINT PROCESSES

Autor(en): Reitzner, Matthias 
Schulte, Matthias
Stichwörter: Central limit theorem; CHAOS; CUMULANTS; FUNCTIONALS; GAUSSIAN FLUCTUATIONS; GEOMETRIC RANDOM GRAPHS; Malliavin calculus; Mathematics; PLANE; Poisson point process; PROBABILITY; SPACE; Statistics & Probability; Stein's method; U-statistic; WIENER; Wiener-Ito chaos expansion
Erscheinungsdatum: 2013
Herausgeber: INST MATHEMATICAL STATISTICS
Journal: ANNALS OF PROBABILITY
Volumen: 41
Ausgabe: 6
Startseite: 3879
Seitenende: 3909
Zusammenfassung: 
A U-statistic of a Poisson point process is defined as the sum Sigma f(x(1),...,x(k)) over all (possibly infinitely many) k-tuples of distinct points of the point process. Using the Malliavin calculus, the Wiener-Ito chaos expansion of such a functional is computed and used to derive a formula for the variance. Central limit theorems for U-statistics of Poisson point processes are shown, with explicit bounds for the Wasserstein distance to a Gaussian random variable. As applications, the intersection process of Poisson hyperplanes and the length of a random geometric graph are investigated.
ISSN: 00911798
DOI: 10.1214/12-AOP817

Show full item record

Page view(s)

2
Last Week
0
Last month
0
checked on Mar 2, 2024

Google ScholarTM

Check

Altmetric