La descente et la montée étendues: the spatially <Emphasis Type="Bold">d</Emphasis>-anisotropic and the spatio-temporal case |
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| Authors: | E Porcu P Gregori J Mateu |
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| Institution: | (1) Department of Mathematics, Universitat Jaume I, Campus Riu Sec, 12071 Castellón, Spain |
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| Abstract: | There is a great demand for statistical modeling of phenomena that evolve in both space and time, and thus, there is a growing
literature on correlation function models for spatio-temporal processes. In particular, various properties of these correlation
functions have been studied only for the merely spatial or temporal case, fact that constitutes a strong motivation for our
work. The goal of this paper is to inspect some properties, obtained with respect to partial differentiation and integration,
of stationary spatio-temporal correlation functions for which anisotropy is obtained through isotropy between components as
in Fernández-Casal et al. (Stat Comput 13(2):127–136, 2003). We show that through partial differentiation and integration it is possible to obtain permissible spatio-temporal correlation
functions in the space–time domain. Other new results regard specific classes of space–time correlations introduced in recent
literature. A curious result arises by differentiating scale mixtures of Euclid’s hat.
Work partially funded by grant MTM2004-06231 from the Spanish Ministery of Science and Education. |
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| Keywords: | Descente d-Anisotropy Euclid’ s hat Montée Positive definite functions |
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