Mixing properties of multivariate infinitely divisible random fields
File(s)
Author(s)
Passeggeri, Riccardo
Veraart, Almut
Type
Journal Article
Abstract
In this work we present different results concerning mixing properties of multivariate infinitely divis-
ible (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 sim-
ple 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.
ible (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 sim-
ple 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.
Date Issued
2019-12
Date Acceptance
2018-09-17
Citation
Journal of Theoretical Probability, 2019, 32 (4), pp.1845-1879
ISSN
0894-9840
Publisher
Springer Verlag
Start Page
1845
End Page
1879
Journal / Book Title
Journal of Theoretical Probability
Volume
32
Issue
4
Copyright Statement
© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Identifier
https://link.springer.com/article/10.1007%2Fs10959-018-0864-7
Subjects
Statistics & Probability
0104 Statistics
0101 Pure Mathematics
Publication Status
Published
Date Publish Online
2018-10-01