TY - JOUR
T1 - New classes of spectral densities for lattice processes and random fields built from simple univariate margins
AU - Porcu, Emilio
AU - Mateu, Jorge
AU - Gregori, Pablo
AU - Ostoja-Starzewski, Martin
N1 - This study was initiated when Emilio Porcu was research fellow at the Universitat Jaume I, department of Mathematics. He also acknowledges the support of the research fund FOR-916 Statistical Regularization. Jorge Mateu and Pablo Gregori acknowledge the support of MTM2010-14961 from the Spanish Ministry of Science and Education.
PY - 2012/5
Y1 - 2012/5
N2 - Quasi arithmetic and Archimedean functionals are used to build new classes of spectral densities for processes defined on any d-dimensional lattice ℤ d and random fields defined on the d-dimensional Euclidean space ℝ d12, 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.
AB - Quasi arithmetic and Archimedean functionals are used to build new classes of spectral densities for processes defined on any d-dimensional lattice ℤ d and random fields defined on the d-dimensional Euclidean space ℝ d12, 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.
KW - Archimedeanity
KW - Lattice processes
KW - Nonseparability
KW - Quasi arithmetic functionals
KW - Random fields
KW - Spectral densities
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U2 - 10.1007/s00477-012-0572-2
DO - 10.1007/s00477-012-0572-2
M3 - Article
AN - SCOPUS:84859438239
SN - 1436-3240
VL - 26
SP - 479
EP - 490
JO - Stochastic Environmental Research and Risk Assessment
JF - Stochastic Environmental Research and Risk Assessment
IS - 4
ER -