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  • A review of approximations

    Rights statement: The final publication is available at Springer via http://dx.doi.org/10.1007/s11144-018-1351-y

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

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<mark>Journal publication date</mark>04/2018
<mark>Journal</mark>Reaction Kinetics, Mechanisms and Catalysis
Issue number2
Volume123
Number of pages24
Pages (from-to)289-312
Publication StatusPublished
Early online date24/01/18
<mark>Original language</mark>English

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.

Bibliographic note

The final publication is available at Springer via http://dx.doi.org/10.1007/s11144-018-1351-y