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Analysis of Stochastic Chemical Reaction Networks with a Hierarchy of Timescales
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Journal Article
Analysis of Stochastic Chemical Reaction Networks with a Hierarchy of Timescales
2025
Overview
We investigate a class of stochastic chemical reaction networks withn≥1chemical speciesS₁ ,S_(n) , and whose complexes are only of the formkᵢSᵢ ,i=1 ,n , where(kᵢ)are integers. The time evolution of these CRNs is driven by the kinetics of the law of mass action. A scaling analysis is done when the rates of external arrivals of chemical species are proportional to a large scaling parameterN . A natural hierarchy of fast processes, a subset of the coordinates of(Xᵢ(t)) , is determined by the values of the mappingi↦kᵢ . We show that the scaled vector of coordinatesisuch thatkᵢ=1and the scaled occupation measure of the other coordinates are converging in distribution to a deterministic limit asNgets large. The proof of this result is obtained by establishing a functional equation for the limiting points of the occupation measure, by an induction on the hierarchy of timescales and with relative entropy functions.
Publisher
Springer Verlag
Subject
