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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 VV of the Poisson equation LV+f=0LV + f=0 where LL is the backward generator of an irreducible (finite) Markov jump process and ff is a given centered state function. Bounds on VV 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.

Keywords

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}
}
R2 v1 2026-06-28T13:05:24.590Z