Large deviations for two scale chemical kinetic processes

TL;DR

This paper develops a large deviations framework for two-scale chemical kinetic processes, with applications to genetic switching models, highlighting the convexity of the Hamiltonian and its advantages in rare event simulations.

Contribution

It introduces a rigorous large deviations approach for multiscale chemical kinetics, emphasizing the convex Hamiltonian and improving rare event simulation methods.

Findings

Successful application to genetic switching models with feedbacks

Convexity of the Hamiltonian enhances rare event simulations

Provides a general framework for large deviations in multiscale systems

Abstract

We formulate the large deviations for a class of two scale chemical kinetic processes motivated from biological applications. The result is successfully applied to treat a genetic switching model with positive feedbacks. The corresponding Hamiltonian is convex with respect to the momentum variable as a by-product of the large deviation theory. This property ensures its superiority in the rare event simulations compared with the result obtained by formal WKB asymptotics. The result is of general interest to understand the large deviations for multiscale problems.