Mathematics – Probability
Scientific paper
2005-07-30
Annals of Applied Probability 2006, Vol. 16, No. 4, 1925-1961
Mathematics
Probability
Published at http://dx.doi.org/10.1214/105051606000000420 in the Annals of Applied Probability (http://www.imstat.org/aap/) by
Scientific paper
10.1214/105051606000000420
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.
Ball Karen
Kurtz Thomas G.
Popovic Lea
Rempala Greg
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