An inequality connecting entropy distance, Fisher Information and large deviations

Bastian Hilder (Corresponding author), Mark A. Peletier (Corresponding author), Upanshu Sharma, Oliver Tse

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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.

Original languageEnglish
Pages (from-to)2596-2638
Number of pages43
JournalStochastic Processes and their Applications
Volume130
Issue number5
DOIs
Publication statusPublished - May 2020

Keywords

  • Fisher Information
  • Large deviations
  • Markov jump process
  • Relative entropy

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