Information and estimation in Fokker-Planck channels

Andre Wibisono; Varun Jog; Po-Ling Loh

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arXiv · 1702.03656

Information and estimation in Fokker-Planck channels

Andre Wibisono·Varun Jog·Po-Ling Loh

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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.

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BibTeX RIS

Andre Wibisono, Varun Jog, Po-Ling Loh. 2017-02-13. Information and estimation in Fokker-Planck channels. https://arxiv.org/abs/1702.03656

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