New classes of spectral densities for lattice processes and random fields built from simple univariate margins

Emilio Porcu, Jorge Mateu, Pablo Gregori, Martin Ostoja-Starzewski

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)479-490
Number of pages12
JournalStochastic Environmental Research and Risk Assessment
Volume26
Issue number4
DOIs
StatePublished - May 2012

Keywords

  • Archimedeanity
  • Lattice processes
  • Nonseparability
  • Quasi arithmetic functionals
  • Random fields
  • Spectral densities

ASJC Scopus subject areas

  • Environmental Engineering
  • Environmental Chemistry
  • Safety, Risk, Reliability and Quality
  • Water Science and Technology
  • Environmental Science(all)

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