An inequality connecting entropy distance, Fisher Information and large deviations

Bastian Hilder, Mark A. Peletier, Upanshu Sharma and Oliver Tse

Stochastic Processes and their Applications, 2020, vol. 130, issue 5, 2596-2638

Abstract: In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large deviation rate functional. In addition to possessing various favourable properties, we show that this generalised Fisher Information converges to the classical Fisher Information in an appropriate limit. We then use this generalised Fisher Information and the aforementioned inequality to qualitatively study coarse-graining problems for jump processes on discrete spaces.

Keywords: Markov jump process; Relative entropy; Fisher Information; Large deviations (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2019.07.012

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