An inequality connecting entropy distance, Fisher Information and large deviations

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

Research output: Contribution to journalArticleAcademicpeer-review

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
JournalStochastic Processes and their Applications
DOIs
Publication statusAccepted/In press - 1 Jan 2019

Fingerprint

Fisher Information
Large Deviations
Entropy
Markov Jump Processes
Coarse-graining
Jump Process
Relative Entropy
Countable
State Space
Converge

Keywords

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

Cite this

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An inequality connecting entropy distance, Fisher Information and large deviations. / Hilder, Bastian (Corresponding author); Peletier, Mark A. (Corresponding author); Sharma, Upanshu; Tse, Oliver.

In: Stochastic Processes and their Applications, 01.01.2019.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Sharma, Upanshu

AU - Tse, Oliver

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KW - Markov jump process

KW - Relative entropy

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