Large deviations theory for markov jump models of chemical reaction networks


Journal Article

© Institute of Mathematical Statistics, 2018. 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.

Full Text

Duke Authors

Cited Authors

  • Agazzi, A; Dembo, A; Eckmann, JP

Published Date

  • June 1, 2018

Published In

Volume / Issue

  • 28 / 3

Start / End Page

  • 1821 - 1855

International Standard Serial Number (ISSN)

  • 1050-5164

Digital Object Identifier (DOI)

  • 10.1214/17-AAP1344

Citation Source

  • Scopus