Bounding the coarse graining error in hidden Markov dynamics

TL;DR

This paper derives finite-time bounds on the error introduced when approximating coarse-grained Markov dynamics, applicable to non-reversible systems and probabilistic mappings, enhancing understanding of coarse graining in Markov processes.

Contribution

It provides the first finite-time bounds on coarse graining errors in Markov dynamics, including non-reversible cases and probabilistic state mappings.

Findings

Finite-time bounds on coarse graining error derived

Results applicable to non-reversible Markov processes

Error bounds hold for probabilistic state mappings

Abstract

Lumping a Markov process introduces a coarser level of description that is useful in many contexts and applications. The dynamics on the coarse grained states is often approximated by its Markovian component. In this letter we derive finite-time bounds on the error in this approximation. These results hold for non-reversible dynamics and for probabilistic mappings between microscopic and coarse grained states.