Stochastic Wiener filter in the white noise space

Opuscula Mathematica

article

Daniel Alpay (corresponding author)¹  Ariel Pinhas² 

[1] Schmid College of Science and Technology, Chapman University, One University Drive Orange;Department of Mathematics, Ben-Gurion University of the Negev

关键词: Wiener filter;    white noise space;    Wick product;    stochastic distribution.;   

DOI  :  10.7494/OpMath.2020.40.3.323

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

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.

【 授权许可】

CC BY-NC