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August 2015 Modulus of continuity of some conditionally sub-Gaussian fields, application to stable random fields
Hermine Biermé, Céline Lacaux
Bernoulli 21(3): 1719-1759 (August 2015). DOI: 10.3150/14-BEJ619

Abstract

In this paper, we study modulus of continuity and rate of convergence of series of conditionally sub-Gaussian random fields. This framework includes both classical series representations of Gaussian fields and LePage series representations of stable fields. We enlighten their anisotropic properties by using an adapted quasi-metric instead of the classical Euclidean norm. We specify our assumptions in the case of shot noise series where arrival times of a Poisson process are involved. This allows us to state unified results for harmonizable (multi)operator scaling stable random fields through their LePage series representation, as well as to study sample path properties of their multistable analogous.

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Hermine Biermé. Céline Lacaux. "Modulus of continuity of some conditionally sub-Gaussian fields, application to stable random fields." Bernoulli 21 (3) 1719 - 1759, August 2015. https://doi.org/10.3150/14-BEJ619

Information

Received: 1 January 2013; Revised: 1 December 2013; Published: August 2015
First available in Project Euclid: 27 May 2015

zbMATH: 1323.60072
MathSciNet: MR3352059
Digital Object Identifier: 10.3150/14-BEJ619

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

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Vol.21 • No. 3 • August 2015
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