Thomas Kurtz

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  Identifying separated time scales in stochastic models of reaction networks
  Thomas Kurtz
  For chemical reaction networks in biological cells, reaction rates and chemical species numbers may vary over several orders of magnitude. Combined, these large variations can lead to subnetworks operating on very different time scales. Separation of time scales has been exploited in many contexts as a basis for reducing the complexity of dynamic models, but the interaction of the rate constants and the species numbers makes identifying the appropriate time scales tricky at best. Some systematic approaches to this identification will be discussed and illustrated by application to one or more complex reaction network models.
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  Derivation of deterministic models from stochastic models
  Thomas Kurtz
  Beginning with the simple derivation of the (deterministic) law of mass action from Markov chain models of chemical reaction networks, we will illustrate the derivation of deterministic, piecewise deterministic, and stochastically perturbed deterministic models from increasingly complex stochastic models. The arguments exploit asymptotic properties of stochastic equations and limits of exchangeable systems. The last method will be applied to obtain results of Robert and Touboul for a neural network model.