TY  - JOUR
ID  - Alpay2020
LB  - Alpay2020
AU  - Alpay, Daniel
AU  - Pinhas, Ariel
TI  - Stochastic Wiener filter in the white noise space
ST  - Stochastic Wiener filter in the white noise space
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 3
SP  - 323
EP  - 339
DO  - https://doi.org/10.7494/OpMath.2020.40.3.323
UR  - https://doi.org/10.7494/OpMath.2020.40.3.323
AB  - 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.
KW  - Wiener filter
KW  - white noise space
KW  - Wick product
KW  - stochastic distribution
SN  - 1232-9274
ER  -