WIAS Preprint No. 2816, (2021)

Large deviations for Markov jump processes with uniformly diminishing rates



Authors

  • Agazzi, Andrea
  • Andreis, Luisa
  • Patterson, Robert I. A.
    ORCID: 0000-0002-3583-2857
  • Renger, D. R. Michiel
    ORCID: 0000-0003-3557-3485

2020 Mathematics Subject Classification

  • 60F10 60J76 80A30

Keywords

  • Large deviations, chemical reaction networks, jump Markov processes, Freidlin--Wentzell theory

DOI

10.20347/WIAS.PREPRINT.2816

Abstract

We prove a large-deviation principle (LDP) for the sample paths of jump Markov processes in the small noise limit when, possibly, all the jump rates vanish uniformly, but slowly enough, in a region of the state space. We further show that our assumptions on the decay of the jump rates are optimal. As a direct application of this work we relax the assumptions needed for the application of LDPs to, e.g., Chemical Reaction Network dynamics, where vanishing reaction rates arise naturally particularly the context of Mass action kinetics.

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