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November 2006 Asymptotic analysis of multiscale approximations to reaction networks
Karen Ball, Thomas G. Kurtz, Lea Popovic, Greg Rempala
Ann. Appl. Probab. 16(4): 1925-1961 (November 2006). DOI: 10.1214/105051606000000420

Abstract

A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as possible transitions of the chain. In many cases of biological interest some of the chemical species in the network are present in much greater abundance than others and reaction rate constants can vary over several orders of magnitude. We consider approaches to approximation of such models that take the multiscale nature of the system into account. Our primary example is a model of a cell’s viral infection for which we apply a combination of averaging and law of large number arguments to show that the “slow” component of the model can be approximated by a deterministic equation and to characterize the asymptotic distribution of the “fast” components. The main goal is to illustrate techniques that can be used to reduce the dimensionality of much more complex models.

Citation

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Karen Ball. Thomas G. Kurtz. Lea Popovic. Greg Rempala. "Asymptotic analysis of multiscale approximations to reaction networks." Ann. Appl. Probab. 16 (4) 1925 - 1961, November 2006. https://doi.org/10.1214/105051606000000420

Information

Published: November 2006
First available in Project Euclid: 17 January 2007

zbMATH: 1118.92031
MathSciNet: MR2288709
Digital Object Identifier: 10.1214/105051606000000420

Subjects:
Primary: 60F17, 60J27, 60J80, 80A30, 92C45

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.16 • No. 4 • November 2006
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