De Bruijn identities in different Markovian channels

Date

2023-02-06

Authors

Emamirad, Hassan
Rougirel, Arnaud

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

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.

Description

Keywords

Fokker Planck, Relative Fisher information, Kullback-Leibler divergence

Citation

Emamirad, H., & Rougirel, A. (2023). De Bruijn identities in different Markovian channels. <i>Electronic Journal of Differential Equations, 2023</i>(12), pp. 1-11.

Rights

Attribution 4.0 International

Rights Holder

Rights License