A short memory condition for infinitely divisible random fields

TL;DR

This paper provides a sufficient condition for short-range dependence in stationary infinitely divisible random fields, extending existing concepts and aligning with previous results in special cases like symmetric stable moving averages.

Contribution

It introduces a new short memory condition for infinitely divisible random fields, generalizing prior dependence concepts and connecting with established results in specific cases.

Findings

New sufficient condition for short-range dependence

Condition aligns with previous results for symmetric stable cases

Enhances understanding of dependence structures in random fields

Abstract

This small note yields a sufficient condition for the short range dependence of measurable stationary infinitely divisible moving average random fields with $d$--dimensional index space. Here, the short/long range dependence concept in borrowed from the paper of Kulik and Spodarev (2021). In the special case of symmetric stable moving averages, our new condition coincides with the one from the paper of Makogin et al. (2021).