A note on decoupling of local and global behaviours for the Dagum Random Field

J. Mateu, E. Porcu, O. Nicolis

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

Self-affinity versus decoupling: this dichotomy represents a breakthrough with respect to the previous literature, that has grown under the dogma of self-affinity. The word decoupling refers to those correlation functions allowing to treat independently the Hausdorff-Besicovitch dimension and Hurst effect parameters. The former is a roughness measure associated to profiles or surfaces. The latter reflects possible persistent or antipersistent behaviours of the associated random process or random field. Thus, the decoupling philosophy opens new avenues for the analysis and interpretation of local and global properties of random fields. In this paper, we introduce a new class of isotropic correlation functions, called Dagum, show its permissibility on any n-dimensional space, and analyse its attitudes with respect to decoupling. Interesting aspects arise from an intensive simulation study, conducted in one and two dimensions. In particular, it seems that the decoupling attitude may depend on the space dimension.

Original languageEnglish
Pages (from-to)320-329
Number of pages10
JournalProbabilistic Engineering Mechanics
Volume22
Issue number4
DOIs
Publication statusPublished - 1 Oct 2007

Keywords

  • Continuum mechanics
  • Correlation function
  • Dagum random field
  • Decoupling
  • Fractal structure
  • Hausdorff-Besicovitch dimension
  • Hurst effect
  • Isotropy
  • Self-affinity

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Civil and Structural Engineering
  • Nuclear Energy and Engineering
  • Aerospace Engineering
  • Condensed Matter Physics
  • Ocean Engineering
  • Mechanical Engineering

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