New classes of spectral densities for lattice processes and random fields built from simple univariate margins |
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Authors: | Emilio Porcu Jorge Mateu Pablo Gregori Martin Ostoja-Starzewski |
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Affiliation: | 1.University of G?ttingen, Institut für Mathematische Stochastik,G?ttingen,Germany;2.Department of Mathematics,Universitat Jaume I,Castellón,Spain;3.IMAC Institut Universitari de Matemtiques i Aplicacions de Castelló,Castellón,Spain;4.Department of Mechanical Science and Engineering,Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign,Urbana,USA |
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Abstract: | Quasi arithmetic and Archimedean functionals are used to build new classes of spectral densities for processes defined on any d-dimensional lattice mathbbZd{mathbb{Z}^d} and random fields defined on the d-dimensional Euclidean space mathbbRd{mathbb{R}^d}, given simple margins. We discuss the mathematical features of the proposed constructions, and show rigorously as well as through examples, that these new classes of spectra generalize celebrated classes introduced in the literature. Additionally, we obtain permissible spectral densities as linear combinations of quasi arithmetic or Archimedean functionals, whose associated correlation functions may attain negative values or oscillate between positive and negative ones. We finally show that these new classes of spectral densities can be used for nonseparable processes that are not necessarily diagonally symmetric. |
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