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ℓ1-symmetric vector random fields

Fangfang Wang and Chunsheng Ma

Stochastic Processes and their Applications, 2019, vol. 129, issue 7, 2466-2484

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.

Keywords: Covariance matrix function; Cross covariance; Direct covariance; ℓ1-norm; Elliptically contoured random field; Infinitely divisible; Lévy process; Pólya-type function (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.07.012

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