# Large deviations theory for Markov jump models of chemical reaction networks

Source: [Large deviations theory for Markov jump models of chemical reaction networks](<https://www.sota2.com/research/paper/68fa54441e209131ce98a335>)

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

Data updated: 2025-10-25T12:54:30.398Z

Authors: Andrea Agazzi, Amir Dembo, Jean-Pierre Eckmann

Published: 2017-01-09T10:41:02.000Z

## Abstract

We prove a sample path Large Deviation Principle (LDP) for a class of jump processes whose rates are not uniformly Lipschitz continuous in phase space. Building on it we further establish the corresponding Wentzell-Freidlin (W-F) (infinite time horizon) asymptotic theory. These results apply to jump Markov processes that model the dynamics of chemical reaction networks under mass action kinetics, on a microscopic scale. We provide natural sufficient topological conditions for the applicability of our LDP and W-F results. This then justifies the computation of non-equilibrium potential and exponential transition time estimates between different attractors in the large volume limit, for systems that are beyond the reach of standard chemical reaction network theory.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1701.02126>)

[PDF](<https://arxiv.org/pdf/1701.02126.pdf>)