Modulus of continuity of some conditionally sub-Gaussian fields, application to stable random fields

TL;DR

This paper investigates the continuity and convergence of conditionally sub-Gaussian and stable random fields, using anisotropic metrics and series representations, to unify understanding of their path properties and scaling behaviors.

Contribution

It introduces a unified framework for analyzing the modulus of continuity of various stable and sub-Gaussian fields using adapted quasi-metrics and series representations.

Findings

Unified results for stable random fields via LePage series

Analysis of anisotropic properties using quasi-metrics

Sample path properties of multistable fields studied

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.