Spectrum of Periodically Correlated Fields

Authors

  • Dominique Dehay Institut de Recherche Mathématique de Rennes
  • Harry Hurd
  • Andrzej Makagon

Keywords:

Periodically correlated processes, Stochastic processes and fields, Harmonizable processes, Spectrum, Shift operator, LCA group, Fourier transform

Abstract

The paper deals with Hilbert space valued fields over any locally compact Abelian group G, in particular over G = Zn xRm, which are periodically correlated (PC) with respect to a closed subgroup of G. PC fields can be regarded as multi-parameter extensions of PC processes. We study structure, covariance function, and an analogue of the spectrum for such fields. As an example a weakly PC field over Z2 is thoroughly examined.

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Published

2014-08-01

Issue

Section

Mathematical Statistics

How to Cite

Spectrum of Periodically Correlated Fields. (2014). European Journal of Pure and Applied Mathematics, 7(3), 343-368. https://ejpam.com/index.php/ejpam/article/view/1995

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