Mixing Properties of Multivariate Infinitely Divisible Random Fields

Riccardo Passeggeri () and Almut Veraart
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Riccardo Passeggeri: Imperial College London

Journal of Theoretical Probability, 2019, vol. 32, issue 4, 1845-1879

Abstract: 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.

Keywords: Multivariate random field; Infinitely divisible; Mixed moving average; Lévy process; Mixing; Weak mixing; Ergodicity; 60E07; 37A25; 60G60; 62M40; 60G10 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-018-0864-7

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