The exponential family of Markov chains and its information geometry

TL;DR

This paper extends the concept of exponential families to Markov chains and applies information geometry to analyze their divergence rates, providing a geometric perspective on Markov chain properties.

Contribution

It introduces a new definition of exponential family for Markov chains and demonstrates the application of information geometry to this framework.

Findings

Extended properties of exponential families to Markov chains

Applied information geometry to characterize divergence rates

Provided a differential geometric viewpoint on Markov chain divergence

Abstract

We introduce a new definition of exponential family of Markov chains, and show that many characteristic properties of the usual exponential family of probability distributions are properly extended to Markov chains. The method of information geometry is effectively applied to our framework, which enables us to characterize the divergence rate of Markov chain from a differential geometric viewpoint.