A refined mean field approximation of synchronous discrete-time population models

Abstract : Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be expressed as an ordinary differential equation. When the objects are (clock-) synchronous the mean field approximation is a discrete time dynamical system. We focus on the latter. We study the accuracy of mean field approximation when this approximation is a discrete-time dynamical system. We extend a result that was shown for the continuous time case and we prove that expected performance indicators estimated by mean field approximation are $O(1/N)$-accurate. We provide simple expressions to effectively compute the asymptotic error of mean field approximation, for finite time-horizon and steady-state, and we use this computed error to propose what we call a \emph{refined} mean field approximation. We show, by using a few numerical examples, that this technique improves the quality of approximation compared to the classical mean field approximation, especially for relatively small population sizes.
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https://hal.inria.fr/hal-01845235
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Submitted on : Friday, July 20, 2018 - 1:04:59 PM
Last modification on : Thursday, October 11, 2018 - 8:48:05 AM
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Nicolas Gast, Diego Latella, Mieke Massink. A refined mean field approximation of synchronous discrete-time population models. Performance Evaluation, Elsevier, 2018, pp.1-27. 〈10.1016/j.peva.2018.05.002〉. 〈hal-01845235〉

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