A Refined Mean Field Approximation for Synchronous Population Processes

International audienceMean 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 synchronous the mean field approximation is a discrete time dynamical system. In this paper, we focus on the latter. We show that, similarly to the asynchronous case, the mean field approximation of a synchronous population can be refined by a term in 1/N. Our result holds for finite time-horizon and steady-state. We provide two examples that illustrate the approach and its limit