Communications in Mathematical Sciences

Volume 15 (2017)

Number 1

Large deviations for two-scale chemical kinetic processes

Pages: 123 – 163

DOI: http://dx.doi.org/10.4310/CMS.2017.v15.n1.a6

Authors

Tiejun Li (LMAM and School of Mathematical Sciences, Peking University, Beijing, China)

Feng Lin (LMAM and School of Mathematical Sciences, Peking University, Beijing, China)

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 byproduct of the large deviation theory. This property ensures its superiority in the rare event simulations compared to the result obtained by formal WKB asymptotics. The result is of general interest in understanding the large deviations for multiscale problems.

Keywords

chemical kinetic processes, two-scale large deviations, rare events, genetic switching

2010 Mathematics Subject Classification

60F10, 60J75, 62P10, 92C37

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Published 10 January 2017