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
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.
Appeared in
- Stochastic Process. Appl., 152 (2022), pp. 533--559, DOI 10.1016/j.spa.2022.06.017 .
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