Document Type
Article
Publication Date
4-4-2020
Abstract
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.
Recommended Citation
Daniel Alpay, Ariel Pinhas, Stochastic Wiener filter in the white noise space, Opuscula Math. 40, no. 3 (2020), 323-339, https://doi.org/10.7494/OpMath.2020.40.3.323
Peer Reviewed
1
Copyright
The authors
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Comments
This article was originally published in Opuscula Mathematica, volume 40, issue 3, in 2020. https://doi.org/10.7494/OpMath.2020.40.3.323