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Zbl 1161.60314
Lim, S.C.; Teo, L.P.
Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure. (English)
[J] Stochastic Processes Appl. 119, No. 4, 1325-1356 (2009). ISSN 0304-4149

Summary: Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the spectral densities of these random fields are studied. The associated self-similar random fields obtained by applying the Lamperti transformation to GFGCC and GSGCC are studied.

MSC 2000:: *60G10 Stationary processes
60G17 Sample path properties
60G60 Random fields

Keywords: Gaussian field with generalized Cauchy covariance; Gaussian sheet with generalized Cauchy covariance; self-similarity; long/short range dependence; Lamperti transform

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