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Information and estimation in Fokker-Planck channels (1702.03656v1)
Published 13 Feb 2017 in cs.IT, math.IT, math.ST, and stat.TH
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.