Stochastic modeling of the anaeorobic model AM2b: Models at different scales

Abstract : The AM28 model is conventionally represented, in large population, as a system of ordinary differential equations. Our goal is to build several models at different scales. At the microscopic scale (the scale of the individual), we propose a pure jump stochastic model. This model can be exactly simulated. However, when the size of the population is large that type of exact simulation is not feasible, hence we propose approximated simulation methods in discrete time, of the Pois-son type or of the diffusive type. The diffusive type of approximated simulation method can be seen as a discretization of a stochastic differential equation. Finally, we present informally a law of large numbers/central limit theorem of the functional type and how they can be used to provide models at different scales or hybrid models.
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https://hal.inria.fr/hal-01406450
Contributor : Fabien Campillo <>
Submitted on : Thursday, December 1, 2016 - 11:09:07 AM
Last modification on : Saturday, January 27, 2018 - 1:31:37 AM

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Fabien Campillo, Mohsen Chebbi, Salwa Toumi. Stochastic modeling of the anaeorobic model AM2b: Models at different scales. 13th Africain Conference on Research in Computer Science and Applied Mathematics (CARI 2016), Oct 2016, Tunis, Tunisia. ⟨hal-01406450⟩

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