Stochastic Wiener filter in the white noise space

• Autorzy: Alpay Daniel , Pinhas Ariel

Identyfikatory

DOI

10.7494/OpMath.2020.40.3.323

• Języki publikacji: EN

Abstrakty

EN

. In this paper we introduce a new approach to the study of filtering theory by allowing the system's parameters to have a random character. We use Hida's white noise space theory to give an alternative characterization and a proper generalization to the Wiener filter over a suitable space of stochastic distributions introduced by Kondratiev. The main idea throughout this paper is to use the nuclearity of this space in order to view the random variables as bounded multiplication operators (with respect to the Wick product) between Hilbert spaces of stochastic distributions. This allows us to use operator theory tools and properties of Wiener algebras over Banach spaces to proceed and characterize the Wiener filter equations under the underlying randomness assumptions.

Słowa kluczowe

EN

Wiener filter; white noise space; Wick product; stochastic distribution

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2020
• Tom: Vol. 40, no. 3
• Strony: 323--339
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Alpay Daniel

• Schmid College of Science and Technology Chapman University One University Drive Orange, California 92866, USA

autor

Pinhas Ariel

• Department of Mathematics Ben-Gurion University of the Negev P.O. Box 653, Beer-Sheva 84105, Israel

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).