Mixing Properties of Multivariate Infinitely Divisible Random Fields

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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
Pages (from-to)1845-1879
Number of pages35
Publication statusPublished - 1 Dec 2019
Externally publishedYes

    Research areas

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

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