Isotropic random fields with infinitely divisible marginal distributions

dc.contributor.authorWang, Fangfang
dc.contributor.authorLeonenko, Nikolai
dc.contributor.authorMa, Chunsheng
dc.descriptionClick on the DOI link to access the article (may not be free).en_US
dc.description.abstractA simple but efficient approach is proposed in this paper to construct the isotropic random field in (d 2), whose univariate marginal distributions may be taken as any infinitely divisible distribution with finite variance. The three building blocks in our building tool box are a second-order Levy process on the real line, a d-variate random vector uniformly distributed on the unit sphere, and a positive random variable that generates a Polya-type function. The approach extends readily to the multivariate case and results in a vector random field in with isotropic direct covariance functions and with any specified infinitely divisible marginal distributions. A characterization of the turning bands simulation feature is also derived for the covariance matrix function of a Gaussian or elliptically contoured random field that is isotropic and mean square continuous in R-d.en_US
dc.description.sponsorshipCardiff Incoming Visiting Fellowship Scheme, International Collaboration Seedcorn Fund, Australian Research Council's Discovery Projects funding scheme (project DP160101366) and project MTM2015-71839-P of MINECO, Spain (co-funded with FEDER funds).en_US
dc.identifier.citationFangfang Wang, Nikolai Leonenko & Chunsheng Ma. Isotropic random fields with infinitely divisible marginal distributions. Stochastic Analysis and Applications, vol. 36:no. 2:pp 189-208en_US
dc.publisherTaylor & Francisen_US
dc.relation.ispartofseriesStochastic Analysis and Applications;v.36:no.2
dc.subjectCovariance matrix functionen_US
dc.subjectCross covarianceen_US
dc.subjectDirect covarianceen_US
dc.subjectElliptically contoured random fielden_US
dc.subjectGaussian random fielden_US
dc.subjectInfinitely divisibleen_US
dc.subjectLevy processen_US
dc.subjectPolya-type functionen_US
dc.subjectTurning bands methoden_US
dc.titleIsotropic random fields with infinitely divisible marginal distributionsen_US
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