Translator Disclaimer
October 2019 Normal convergence of nonlocalised geometric functionals and shot-noise excursions
Raphaël Lachièze-Rey
Ann. Appl. Probab. 29(5): 2613-2653 (October 2019). DOI: 10.1214/18-AAP1445

Abstract

This article presents a complete second-order theory for a large class of geometric functionals on homogeneous Poisson input. In particular, the results do not require the existence of a radius of stabilisation. Hence they can be applied to geometric functionals of spatial shot-noise fields excursions such as volume, perimeter, or Euler characteristic (the method still applies to stabilising functionals). More generally, it must be checked that a local contribution to the functional is not strongly affected under a perturbation of the input far away. In this case, the exact asymptotic variance is given, as well as the likely optimal speed of convergence in the central limit theorem. This goes through a general mixing-type condition that adapts nicely to both proving asymptotic normality and that variance is of volume order.

Citation

Download Citation

Raphaël Lachièze-Rey. "Normal convergence of nonlocalised geometric functionals and shot-noise excursions." Ann. Appl. Probab. 29 (5) 2613 - 2653, October 2019. https://doi.org/10.1214/18-AAP1445

Information

Received: 1 July 2018; Revised: 1 October 2018; Published: October 2019
First available in Project Euclid: 18 October 2019

zbMATH: 07155055
MathSciNet: MR4019871
Digital Object Identifier: 10.1214/18-AAP1445

Subjects:
Primary: 60D05, 60F05, 60G60

Rights: Copyright © 2019 Institute of Mathematical Statistics

JOURNAL ARTICLE
41 PAGES

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

SHARE
Vol.29 • No. 5 • October 2019
Back to Top