Mathematical framework for pseudo-spectra of linear stochastic difference equations

  1. Bujosa Brun, Andrés
  2. Bujosa Brun, Marcos
  3. García Ferrer, Antonio
Revista:
Documentos de Trabajo (ICAE)

ISSN: 2341-2356

Año de publicación: 2013

Número: 13

Páginas: 1-13

Tipo: Documento de Trabajo

DIALNET GOOGLE SCHOLAR lock_openDocta Complutense editor

Otras publicaciones en: Documentos de Trabajo (ICAE)

Resumen

Although spectral analysis of stationary stochastic processes has solid mathematical foundations, this is not always so for the non-stationary case. Here, we establish a sound mathematical framework for the spectral analysis of non-stationary solutions of linear stochastic difference equations. To achieve it, the classical problem is embedded in a wider framework, the Rigged Hilbert space; the Fourier Transform is extended, and a new Extended Fourier Transform pair pseudocovariance function/pseudo-spectrum is defined. Our approach is an extension proper of the classical spectral analysis, where the Fourier Transform pair auto-covariance function/spectrum is a particular case, and consequently spectrum and pseudo-spectrum are identical when the first one is defined.

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