On the Poisson equation for nonreversible Markov jump processes
Probability
2024-04-04 v1 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
We study the solution of the Poisson equation where is the backward generator of an irreducible (finite) Markov jump process and is a given centered state function. Bounds on are obtained using a graphical representation derived from the Matrix Forest Theorem and using a relation with mean first-passage times. Applications include estimating time-accumulated differences during relaxation toward a steady nonequilibrium regime.
Cite
@article{arxiv.2310.19219,
title = {On the Poisson equation for nonreversible Markov jump processes},
author = {Faezeh Khodabandehlou and Christian Maes and Karel Netočný},
journal= {arXiv preprint arXiv:2310.19219},
year = {2024}
}