%0 Generic %1 mozgunov2017review %A Mozgunov, Pavel %A Beccuti, Marco %A Horvath, Andras %A Jaki, Thomas %A Sirovich, Roberta %A Bibbona, Enrico %D 2017 %K random-interest %T A review of the deterministic and diffusion approximations for stochastic chemical reaction networks %U http://arxiv.org/abs/1711.02567 %X This work reviews the deterministic and the stochastic approximations of the stochastic chemical reaction network and explains their application. We, particularly, discuss the added value the diffusion approximation provides for systems with different phenomena, such as deficiency and bistability. It is advocated that the diffusion approximation can be consider as an alternative theoretical approach to study the reaction network rather than only a simulation short cut. We discuss two examples in which the diffusion approximation is able to catch qualitative properties of a reaction network that the deterministic model misses. We provide the explicit construction of the original process and diffusion approximation such that the distance between their trajectories is controlled and demonstrate this construction for the examples. We also discuss the limitations and potentials directions of developments.

@misc{mozgunov2017review, abstract = {This work reviews the deterministic and the stochastic approximations of the stochastic chemical reaction network and explains their application. We, particularly, discuss the added value the diffusion approximation provides for systems with different phenomena, such as deficiency and bistability. It is advocated that the diffusion approximation can be consider as an alternative theoretical approach to study the reaction network rather than only a simulation short cut. We discuss two examples in which the diffusion approximation is able to catch qualitative properties of a reaction network that the deterministic model misses. We provide the explicit construction of the original process and diffusion approximation such that the distance between their trajectories is controlled and demonstrate this construction for the examples. We also discuss the limitations and potentials directions of developments.}, added-at = {2017-11-08T15:10:26.000+0100}, author = {Mozgunov, Pavel and Beccuti, Marco and Horvath, Andras and Jaki, Thomas and Sirovich, Roberta and Bibbona, Enrico}, biburl = {https://www.bibsonomy.org/bibtex/2f9b1897bd7f78d6cc0ee3e97ea166de9/claired}, description = {A review of the deterministic and diffusion approximations for stochastic chemical reaction networks}, interhash = {f42e72ab072404d974914b6e08495a63}, intrahash = {f9b1897bd7f78d6cc0ee3e97ea166de9}, keywords = {random-interest}, note = {cite arxiv:1711.02567}, timestamp = {2017-11-08T15:10:26.000+0100}, title = {A review of the deterministic and diffusion approximations for stochastic chemical reaction networks}, url = {http://arxiv.org/abs/1711.02567}, year = 2017 }