Large deviations theory for Markov jump models of chemical reaction networks

TL;DR

This paper develops a large deviations framework for Markov jump processes modeling chemical reaction networks, enabling analysis of rare events and transition times beyond standard theory.

Contribution

It establishes a sample path Large Deviation Principle and Wentzell-Freidlin asymptotics for jump processes with non-Lipschitz rates in chemical networks.

Findings

Proves LDP for non-Lipschitz jump processes

Derives W-F asymptotics for transition analysis

Provides conditions for applying large deviations to chemical 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.