Hassan Emamirad, Arnaud Rougirel
Abstract:
De Bruijn's identity in information theory states that if u
is the solution of the heat equation, then the time derivative
of the Shannon entropy for this solution is equal to the amount of Fisher
information at u.
In this article, we show how this identity changes if we replace
the heat channel by the Fokker Planck, or passing from Fokker Planck to
Ornstein-Uhlenbeck channels. Through these passages we investigate the
different properties of these solutions.
We exclusively dissect different properties of Ornstein-Uhlenbeck
semigroup given by the Mehler formula expression.
Submitted October 27, 2022. Published February 6, 2023.
Math Subject Classifications: 94A17, 94A40.
Key Words: Fokker Planck; relative Fisher information; Kullback-Leibler divergence.
DOI: https://doi.org/10.58997/ejde.2023.12
Show me the PDF file (304 KB), TEX file for this article.
 |
Hassan Emamirad Laboratoire de Mathématiques Université de Poitiers teleport 2, BP 179 86960 Chassneuil du Poitou, Cedex, France email: emamirad@math.univ-poitiers.fr |
|---|---|
 |
Arnaud Rougirel Laboratoire de Mathématiques Université de Poitiers teleport 2, BP 179 86960 Chassneuil du Poitou, Cedex, France email: rougirel@math.univ-poitiers.fr |
Return to the EJDE web page