Translator Disclaimer
December 2015 Normal approximation for statistics of Gibbsian input in geometric probability
Aihua Xia, J. E. Yukich
Author Affiliations +
Adv. in Appl. Probab. 47(4): 934-972 (December 2015). DOI: 10.1239/aap/1449859795

Abstract

This paper concerns the asymptotic behavior of a random variable Wλ resulting from the summation of the functionals of a Gibbsian spatial point process over windows QλRd. We establish conditions ensuring that Wλ has volume order fluctuations, i.e. they coincide with the fluctuations of functionals of Poisson spatial point processes. We combine this result with Stein's method to deduce rates of a normal approximation for Wλ as λ → ∞. Our general results establish variance asymptotics and central limit theorems for statistics of random geometric and related Euclidean graphs on Gibbsian input. We also establish a similar limit theory for claim sizes of insurance models with Gibbsian input, the number of maximal points of a Gibbsian sample, and the size of spatial birth-growth models with Gibbsian input.

Citation

Download Citation

Aihua Xia. J. E. Yukich. "Normal approximation for statistics of Gibbsian input in geometric probability." Adv. in Appl. Probab. 47 (4) 934 - 972, December 2015. https://doi.org/10.1239/aap/1449859795

Information

Published: December 2015
First available in Project Euclid: 11 December 2015

zbMATH: 1333.60037
MathSciNet: MR3433291
Digital Object Identifier: 10.1239/aap/1449859795

Subjects:
Primary: 60F05
Secondary: 60D05, 60G55

Rights: Copyright © 2015 Applied Probability Trust

JOURNAL ARTICLE
39 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.47 • No. 4 • December 2015
Back to Top