Open Access
Spring and Summer 2017 On high-frequency limits of $U$-statistics in Besov spaces over compact manifolds
Solesne Bourguin, Claudio Durastanti
Illinois J. Math. 61(1-2): 97-125 (Spring and Summer 2017). DOI: 10.1215/ijm/1520046211

Abstract

In this paper, quantitative bounds in high-frequency central limit theorems are derived for Poisson based $U$-statistics of arbitrary degree built by means of wavelet coefficients over compact Riemannian manifolds. The wavelets considered here are the so-called needlets, characterized by strong concentration properties and by an exact reconstruction formula. Furthermore, we consider Poisson point processes over the manifold such that the density function associated to its control measure lives in a Besov space. The main findings of this paper include new rates of convergence that depend strongly on the degree of regularity of the control measure of the underlying Poisson point process, providing a refined understanding of the connection between regularity and speed of convergence in this framework.

Citation

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Solesne Bourguin. Claudio Durastanti. "On high-frequency limits of $U$-statistics in Besov spaces over compact manifolds." Illinois J. Math. 61 (1-2) 97 - 125, Spring and Summer 2017. https://doi.org/10.1215/ijm/1520046211

Information

Received: 17 March 2017; Revised: 15 November 2017; Published: Spring and Summer 2017
First available in Project Euclid: 3 March 2018

zbMATH: 1392.60006
MathSciNet: MR3770838
Digital Object Identifier: 10.1215/ijm/1520046211

Subjects:
Primary: 60B05 , 60F05 , 60G57 , 62E20

Rights: Copyright © 2017 University of Illinois at Urbana-Champaign

Vol.61 • No. 1-2 • Spring and Summer 2017
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