Open Access
Translator Disclaimer
2015 Characterisation of gradient flows on finite state Markov chains
Helge Dietert
Author Affiliations +
Electron. Commun. Probab. 20: 1-8 (2015). DOI: 10.1214/ECP.v20-3521

Abstract

In his 2011 work, Maas has shown that the law of anytime-reversible continuous-time Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. In this work we show the converse to the above by showing that if the relative law of a Markov chain with finite state space evolves like a gradient flow of the relative entropy functional, it must be time-reversible. When we allow general functionals in place of the relative entropy, we show that the law of a Markov chain evolves as gradient flow if and only if the generator of the Markov chain is real diagonalisable. Finally, we discuss what aspects of the functional are uniquely determined by the Markov chain.

Citation

Download Citation

Helge Dietert. "Characterisation of gradient flows on finite state Markov chains." Electron. Commun. Probab. 20 1 - 8, 2015. https://doi.org/10.1214/ECP.v20-3521

Information

Accepted: 29 March 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1327.60146
MathSciNet: MR3327868
Digital Object Identifier: 10.1214/ECP.v20-3521

Subjects:

JOURNAL ARTICLE
8 PAGES


SHARE
Back to Top