# Large deviations for Markov jump processes with uniformly diminishing rates

Source: [Large deviations for Markov jump processes with uniformly diminishing rates](<https://www.sota2.com/research/paper/68fa57df1e209131ce9a9349>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:55:56.878Z

Authors: Andrea Agazzi, Luisa Andreis, Robert I. A. Patterson, D. R. Michiel Renger

Published: 2021-02-25T17:52:40.000Z

## 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 discuss the optimality of our assumptions on the decay of the jump rates. 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2102.13040>)

[PDF](<https://arxiv.org/pdf/2102.13040.pdf>)