A complete characterization of monotonicity equivalence for continuous-time Markov processes

TL;DR

This paper proves Dai Pra et al's conjecture, providing a complete characterization of when monotonicity equivalence holds for continuous-time Markov processes on finite posets, based on their structure.

Contribution

It confirms the conjecture and offers a full classification of posets where monotonicity equivalence is valid, advancing understanding of Markov process monotonicity.

Findings

Monotonicity equivalence holds for W-glued diamond posets.

No other posets with acyclic extensions satisfy the equivalence.

Complete characterization of posets for monotonicity equivalence.

Abstract

Dai Pra et al studied two notions of monotonicity for continuous-time Markov processes on a finite partially ordered set (poset), and conjectured that monotonicity equivalence holds for a poset of W-glued diamond, and that there is no other case when it has no acyclic extension. We proved their conjecture and were able to provide a complete characterization of posets for monotonicity equivalence.