Approximation of Strictly Stationary Banach-Valued Random Sequence by Fourier Integral

Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

This paper is devoted to the approximation of a second-order E-valued strictly stationary random sequence by the Fourier transform of a LE2-valued random measure, where E is a complex separable Banach space. For this purpose, we use the spectral representation of a second order E-valued stationary random function and we introduce a bijective linear operator on LE2 which preserves the norm in the form of a “shift operator” associated with a LE2-valued strictly stationary sequence.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Laboratoire de Statistique et Processus StochastiquesUniversité Djillali LiabèsSidi Bel AbbésAlgeria

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