Large deviations for stochastic models of chemical reaction networks – Andrea Agazzi (Duke University)

Abstract

At the microscopic level, the dynamics of arbitrary networks ofchemicalreactions can be modeled as jump Markov processes whose sample paths converge, in the limit oflargenumber of molecules, to the solutions of a set of algebraic ordinary differential equations. Fluctuations around these asymptotic trajectories and the corresponding phase transitions can in principle be studied throughlargedeviationstheoryin path space, also called Wentzell-Freidlin (W-F)theory. However, the specific form of the jump rates for this family of processes does not satisfy the standard regularity assumptions imposed by suchtheory. This talk discusses how such conditions can be relaxed. In this talk, I will discuss sufficient stability and nondegeneracy conditions on the given family of Markov jump processes to obtain the desired large deviationsestimates, and show how some of these conditions can be translated into structural ones, facilitating their verification for large chemicalnetworks.

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