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Multivariate and multiradial Schoenberg measures with their dimension walks
Ist Teil von
Journal of multivariate analysis, 2015-01, Vol.133, p.251-265
Ort / Verlag
New York: Elsevier Inc
Erscheinungsjahr
2015
Quelle
ScienceDirect
Beschreibungen/Notizen
The paper fixes some important properties of matrix-valued correlation functions associated to Multivariate Gaussian fields in a Euclidean space Rd. In particular, we focus (a) on the isotropic (radially symmetric) case and (b) on anisotropy obtained through isotropy between components of the lag vector. This second case includes, as special case, space–time and fully symmetric correlation functions.
Starting from the multivariate analogue of the Schoenberg integral representation of isotropic correlation functions, we characterize their associated measures, which are called here m-Schoenberg measures. We also propose a new dimension walk for the componentwise isotropic case. Finally, we obtain examples where dimension walks for multivariate correlations are not well defined.