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Mixing Properties of Multivariate Infinitely Divisible Random Fields

Author

Listed:
  • Riccardo Passeggeri

    (Imperial College London)

  • Almut E. D. Veraart

    (Imperial College London)

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.

Suggested Citation

  • Riccardo Passeggeri & Almut E. D. Veraart, 2019. "Mixing Properties of Multivariate Infinitely Divisible Random Fields," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1845-1879, December.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:4:d:10.1007_s10959-018-0864-7
    DOI: 10.1007/s10959-018-0864-7
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    References listed on IDEAS

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    1. Rosinski, Jan & Zak, Tomasz, 1996. "Simple conditions for mixing of infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 277-288, February.
    2. Gross, Aaron, 1994. "Some mixing conditions for stationary symmetric stable stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 51(2), pages 277-295, July.
    3. Jan Rosiński & Tomasz Żak, 1997. "The Equivalence of Ergodicity and Weak Mixing for Infinitely Divisible Processes," Journal of Theoretical Probability, Springer, vol. 10(1), pages 73-86, January.
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    Cited by:

    1. Karling, Maicon J. & Lopes, Sílvia R.C. & de Souza, Roberto M., 2023. "Multivariate α-stable distributions: VAR(1) processes, measures of dependence and their estimations," Journal of Multivariate Analysis, Elsevier, vol. 195(C).

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