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.