Mixing Properties of Multivariate Infinitely Divisible Random Fields

Riccardo Passeggeri*, Almut E.D. Veraart

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Abstract

In this work we present different results concerning mixing properties of multivariate infinitely divisible (ID) stationary random fields. First, we derive some necessary and sufficient conditions for mixing of stationary ID multivariate random fields in terms of their spectral representation. Second, we prove that (linear combinations of independent) mixed moving average fields are mixing. Further, using a simple modification of the proofs of our results, we are able to obtain weak mixing versions of our results. Finally, we prove the equivalence of ergodicity and weak mixing for multivariate ID stationary random fields.

Original languageEnglish
JournalJournal of Theoretical Probability
Volume32
Issue4
Pages (from-to)1845-1879
Number of pages35
ISSN0894-9840
DOIs
Publication statusPublished - 1 Dec 2019
Externally publishedYes

Keywords

  • Ergodicity
  • Infinitely divisible
  • Lévy process
  • Mixed moving average
  • Mixing
  • Multivariate random field
  • Weak mixing

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