English

Large deviations theory for Markov jump models of chemical reaction networks

Probability 2017-10-24 v2 Dynamical Systems Molecular Networks

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.

Keywords

Cite

@article{arxiv.1701.02126,
  title  = {Large deviations theory for Markov jump models of chemical reaction networks},
  author = {Andrea Agazzi and Amir Dembo and Jean-Pierre Eckmann},
  journal= {arXiv preprint arXiv:1701.02126},
  year   = {2017}
}