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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

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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A review of the deterministic and diffusion approximations for stochastic chemical reaction networks. / Mozgunov, Pavel; Beccuti, Marco; Horvath, Andras et al.
In: Reaction Kinetics, Mechanisms and Catalysis, Vol. 123, No. 2, 04.2018, p. 289-312.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Mozgunov, P, Beccuti, M, Horvath, A, Jaki, TF, Sirovich, R & Bibbona, E 2018, 'A review of the deterministic and diffusion approximations for stochastic chemical reaction networks', Reaction Kinetics, Mechanisms and Catalysis, vol. 123, no. 2, pp. 289-312. https://doi.org/10.1007/s11144-018-1351-y

APA

Mozgunov, P., Beccuti, M., Horvath, A., Jaki, T. F., Sirovich, R., & Bibbona, E. (2018). A review of the deterministic and diffusion approximations for stochastic chemical reaction networks. Reaction Kinetics, Mechanisms and Catalysis, 123(2), 289-312. https://doi.org/10.1007/s11144-018-1351-y

Vancouver

Mozgunov P, Beccuti M, Horvath A, Jaki TF, Sirovich R, Bibbona E. A review of the deterministic and diffusion approximations for stochastic chemical reaction networks. Reaction Kinetics, Mechanisms and Catalysis. 2018 Apr;123(2):289-312. Epub 2018 Jan 24. doi: 10.1007/s11144-018-1351-y

Author

Mozgunov, Pavel ; Beccuti, Marco ; Horvath, Andras et al. / A review of the deterministic and diffusion approximations for stochastic chemical reaction networks. In: Reaction Kinetics, Mechanisms and Catalysis. 2018 ; Vol. 123, No. 2. pp. 289-312.

Bibtex

@article{7e69b5ac0b4a43558a898789ca39fc85,
title = "A review of the deterministic and diffusion approximations for stochastic chemical reaction networks",
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.",
keywords = "A review of approximations for stochastic chemical reaction networks, Deficiency, Diffusion Approximation, Hungarian Construction, Reaction Networks, Stochastic Differential Equations",
author = "Pavel Mozgunov and Marco Beccuti and Andras Horvath and Jaki, {Thomas Friedrich} and Roberta Sirovich and Enrico Bibbona",
note = "The final publication is available at Springer via http://dx.doi.org/10.1007/s11144-018-1351-y",
year = "2018",
month = apr,
doi = "10.1007/s11144-018-1351-y",
language = "English",
volume = "123",
pages = "289--312",
journal = "Reaction Kinetics, Mechanisms and Catalysis",
issn = "1878-5190",
publisher = "Springer Netherlands",
number = "2",

}

RIS

TY - JOUR

T1 - A review of the deterministic and diffusion approximations for stochastic chemical reaction networks

AU - Mozgunov, Pavel

AU - Beccuti, Marco

AU - Horvath, Andras

AU - Jaki, Thomas Friedrich

AU - Sirovich, Roberta

AU - Bibbona, Enrico

N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/s11144-018-1351-y

PY - 2018/4

Y1 - 2018/4

N2 - 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.

AB - 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.

KW - A review of approximations for stochastic chemical reaction networks

KW - Deficiency

KW - Diffusion Approximation

KW - Hungarian Construction

KW - Reaction Networks

KW - Stochastic Differential Equations

U2 - 10.1007/s11144-018-1351-y

DO - 10.1007/s11144-018-1351-y

M3 - Journal article

VL - 123

SP - 289

EP - 312

JO - Reaction Kinetics, Mechanisms and Catalysis

JF - Reaction Kinetics, Mechanisms and Catalysis

SN - 1878-5190

IS - 2

ER -