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Andrea Agazzi : Large Deviations Theory for Chemical Reaction Networks

The dynamics of a set of chemical reactions are usually modeled by mass action kinetics as a set of algebraic ordinary differential equations. This model sees the state space of the system as a continuum, whereas chemical reactions represent interactions of a discrete set of molecules. We study large fluctuations of the stochastic mass action kinetics model through Freidlin-Wentzell theory. The application of such a theory to this framework requires justification, in particular because of the non-uniformily Lipschitz character of the model. We therefore find, using tools of Lyapunov stability theory, a set of sufficient conditions for the applicability of large deviations theory to this framework, and prove that such conditions are satisfied by a large class of chemical reaction networks identified exclusively on the base of their topological structure.

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