Ruelle-Bowen continuous-time random walk

TL;DR

This paper introduces a continuous-time Markov jump process on finite graphs that maximizes entropy rate and ensures uniform probability over paths with fixed endpoints and jump counts, extending the Ruelle-Bowen concept.

Contribution

It defines the continuous-time Ruelle-Bowen random walk as the unique maximal entropy jump process on finite graphs, generalizing the discrete-time version.

Findings

Maximal entropy rate among jump processes

Uniform path probability given endpoints and jumps

Extension of Ruelle-Bowen walk to continuous time

Abstract

We define the probability structure of a continuous-time time-homogeneous Markov jump process, on a finite graph, that represents the continuous-time counterpart of the so-called Ruelle-Bowen discrete-time random walk. It constitutes the unique jump process having maximal entropy rate. Moreover, it has the property that, given the number of jumps between any two specified end-points on the graph, the probability of traversing any one of the alternative paths that are consistent with the specified number of jumps and end-points, is the same for all, and thereby depends only on the number of jumps and the end-points and not the particular path being traversed.