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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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