Information and estimation in Fokker-Planck channels
Abstract
We study the relationship between information- and estimation-theoretic quantities in time-evolving systems. We focus on the Fokker-Planck channel defined by a general stochastic differential equation, and show that the time derivatives of entropy, KL divergence, and mutual information are characterized by estimation-theoretic quantities involving an appropriate generalization of the Fisher information. Our results vastly extend De Bruijn's identity and the classical I-MMSE relation.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2017
- DOI:
- 10.48550/arXiv.1702.03656
- arXiv:
- arXiv:1702.03656
- Bibcode:
- 2017arXiv170203656W
- Keywords:
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- Computer Science - Information Theory;
- Mathematics - Statistics Theory