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ℓ1-symmetric vector random fields

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  • Wang, Fangfang
  • Ma, Chunsheng

Abstract

This paper studies the properties of ℓ1-symmetric vector random fields in Rd, whose direct/cross covariances are functions of ℓ1-norm. The spectral representation and a turning bands expression of the covariance matrix function are derived for an ℓ1-symmetric vector random field that is mean square continuous. We also establish an integral relationship between an ℓ1-symmetric covariance matrix function and an isotropic one. In addition, a simple but efficient approach is proposed to construct the ℓ1-symmetric random field in Rd, whose univariate marginal distributions may be taken as arbitrary infinitely divisible distribution with finite variance.

Suggested Citation

  • Wang, Fangfang & Ma, Chunsheng, 2019. "ℓ1-symmetric vector random fields," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2466-2484.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:7:p:2466-2484
    DOI: 10.1016/j.spa.2018.07.012
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    References listed on IDEAS

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    1. Brockwell, Peter J. & Schlemm, Eckhard, 2013. "Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 217-251.
    2. Rustam Ibragimov & Artem Prokhorov, 2017. "Heavy Tails and Copulas:Topics in Dependence Modelling in Economics and Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9644, August.
    3. Brockwell, Peter J. & Lindner, Alexander, 2009. "Existence and uniqueness of stationary Lévy-driven CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2660-2681, August.
    4. Richard Finlay & Thomas Fung & Eugene Seneta, 2011. "Autocorrelation Functions," International Statistical Review, International Statistical Institute, vol. 79(2), pages 255-271, August.
    5. Renxiang Wang & Juan Du & Chunsheng Ma, 2014. "Covariance Matrix Functions of Isotropic Vector Random Fields," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2081-2093, May.
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