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A review of the deterministic and diffusion approximations for stochastic chemical reaction networks

Mozgunov, Pavel and Beccuti, Marco and Horvath, Andras and Jaki, Thomas Friedrich and Sirovich, Roberta and Bibbona, Enrico (2018) A review of the deterministic and diffusion approximations for stochastic chemical reaction networks. Reaction Kinetics, Mechanisms and Catalysis, 123 (2). pp. 289-312. ISSN 1878-5190

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    Abstract

    This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena, such as a deficiency and a bistability. It is advocated that the diffusion approximation can be considered as an alternative theoretical approach to study the reaction networks rather than a simulation shortcut. We discuss two examples in which the diffusion approximation is able to catch qualitative properties of reaction networks that the deterministic model misses. We provide an explicit construction of the original process and the diffusion approximation such that the distance between their trajectories is controlled and demonstrate this construction for the examples. We also discuss the limitations and potential directions of the developments.

    Item Type: Journal Article
    Journal or Publication Title: Reaction Kinetics, Mechanisms and Catalysis
    Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s11144-018-1351-y
    Subjects: ?? A REVIEW OF APPROXIMATIONS FOR STOCHASTIC CHEMICAL REACTION NETWORKSDEFICIENCYDIFFUSION APPROXIMATIONHUNGARIAN CONSTRUCTIONREACTION NETWORKSSTOCHASTIC DIFFERENTIAL EQUATIONS ??
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 89906
    Deposited By: ep_importer_pure
    Deposited On: 25 Jan 2018 11:06
    Refereed?: Yes
    Published?: Published
    Last Modified: 29 Apr 2019 16:46
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/89906

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