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Scaling methods for stochastic chemical reaction networks

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  • Laurence, Lucie
  • Robert, Philippe

Abstract

The asymptotic properties of some Markov processes associated to stochastic chemical reaction networks (CRNs) driven by the kinetics of the law of mass action are analyzed. The scaling regime introduced in the paper assumes that the norm of the initial state is converging to infinity. The reaction rate constants are kept fixed. The purpose of the paper is of showing, with simple examples, a scaling analysis in this context. The main difference with the scalings of the literature is that it does not change the graph structure of the CRN or its reaction rates. Several CRNs are investigated to illustrate the insight that can be gained on the qualitative properties of these networks. A detailed scaling analysis of a CRN with several interesting asymptotic properties, with a bi-modal behavior in particular, is worked out in the last section. Additionally, with several examples, we also show that a stability criterion due to Filonov for positive recurrence of Markov processes may simplify significantly the stability analysis of these networks.

Suggested Citation

  • Laurence, Lucie & Robert, Philippe, 2026. "Scaling methods for stochastic chemical reaction networks," Stochastic Processes and their Applications, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:spapps:v:194:y:2026:i:c:s0304414925002996
    DOI: 10.1016/j.spa.2025.104855
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    References listed on IDEAS

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    1. Anderson, David F. & Cappelletti, Daniele & Kim, Jinsu & Nguyen, Tung D., 2020. "Tier structure of strongly endotactic reaction networks," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7218-7259.
    2. Laurence, Lucie & Robert, Philippe, 2025. "Stochastic chemical reaction networks with discontinuous limits and AIMD processes," Stochastic Processes and their Applications, Elsevier, vol. 186(C).
    3. Eberhard O Voit & Harald A Martens & Stig W Omholt, 2015. "150 Years of the Mass Action Law," PLOS Computational Biology, Public Library of Science, vol. 11(1), pages 1-7, January.
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