Mean-field limit versus small-noise limit for some interacting particle systems

Abstract : In the nonlinear diffusion framework, stochastic processes of McKean-Vlasov type play an important role. In some cases they correspond to processes attracted by their own probability distribution: the so-called self-stabilizing processes. Such diffusions can be obtained by taking the hydrodymamic limit in a huge system of linear diffusions in interaction. In both cases, for the linear and the nonlinear processes, small-noise asymptotics have been emphasized by specific large deviation phenomenons. The natural question, therefore, is: is it possible to interchange the mean-field limit with the small-noise limit ? The aim here is to consider this question by proving that the rate function of the first particle in a mean-field system converges to the rate function of the hydrodynamic limit as the number of particles becomes large.
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Submitted on : Friday, December 8, 2017 - 3:39:45 PM
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  • HAL Id : hal-01060199, version 2
  • ARXIV : 1409.1159


Samuel Herrmann, Julian Tugaut. Mean-field limit versus small-noise limit for some interacting particle systems. Communications on Stochastic Analysis, Serials Publications, 2016, 10 (1), pp.39-55. ⟨hal-01060199v2⟩



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