The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 28, Number 3 (2018), 1821-1855.
Large deviations theory for Markov jump models of chemical reaction networks
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 nonequilibrium 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.
Ann. Appl. Probab., Volume 28, Number 3 (2018), 1821-1855.
Received: January 2017
Revised: August 2017
First available in Project Euclid: 1 June 2018
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Agazzi, Andrea; Dembo, Amir; Eckmann, Jean-Pierre. Large deviations theory for Markov jump models of chemical reaction networks. Ann. Appl. Probab. 28 (2018), no. 3, 1821--1855. doi:10.1214/17-AAP1344. https://projecteuclid.org/euclid.aoap/1527840033