On uniform propagation of chaos

Jamil Salhi, James MacLaurin, Salwa Toumi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper we obtain a time-uniform propagation estimate for a system of interacting diffusion processes. Using a well defined metric function h, our result guarantees a time-uniform estimate for the convergence of a class of interacting stochastic differential equations towards their mean field limit, under conditions that ensure that the decay associated to the internal dynamics term dominates the interaction and noise terms. Our result should have diverse applications, particularly in neuroscience, and allows for models more elaborate than the one of Wilson and Cowan. In particular, the internal dynamics need not be that of linear decay.

Original languageEnglish (US)
Pages (from-to)49-60
Number of pages12
JournalStochastics
Volume90
Issue number1
DOIs
StatePublished - Jan 2 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation

Keywords

  • McKean–Vlasov equations
  • Stochastic differential equation
  • interacting diffusion
  • mean fields
  • neural network
  • uniform propagation of chaos

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