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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [27 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01060199
Contributor : Samuel Herrmann <>
Submitted on : Friday, December 8, 2017 - 3:39:45 PM
Last modification on : Monday, May 13, 2019 - 11:19:32 AM
Long-term archiving on : Friday, March 9, 2018 - 12:11:10 PM

File

Convergence.2016.06.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01060199, version 2
  • ARXIV : 1409.1159

Citation

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⟩

Share

Metrics

Record views

177

Files downloads

131