On uniform propagation of chaos |
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Authors: | Jamil Salhi James MacLaurin Salwa Toumi |
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Institution: | 1. Inria Sophia Antipolis Méditerranée - Neuromathcomp Project Team, Cote D’Azur, France.;2. School of Physics, University of Sydney, Sydney, Australia.;3. ENIT - LAMSIN, Tunis, Tunisia. |
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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. |
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Keywords: | Stochastic differential equation mean fields McKean–Vlasov equations interacting diffusion uniform propagation of chaos neural network |
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