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Propagation of chaos for mean field rough differential equations

Abstract : We address propagation of chaos for large systems of rough differential equations associated with random rough differential equations of mean field type. We prove propagation of chaos, and provide also an explicit optimal convergence rate. The analysis is based upon the tools we developed in our companion paper for solving mean field rough differential equations and in particular upon a corresponding version of the Itô-Lyons continuity theorem. The rate of convergence is obtained by a coupling argument developed first by Sznitman for particle systems with Brownian inputs.
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Submitted on : Wednesday, October 30, 2019 - 1:55:28 PM
Last modification on : Thursday, January 20, 2022 - 9:02:01 AM

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Ismaël Bailleul, Rémi Catellier, François Delarue. Propagation of chaos for mean field rough differential equations. Annals of Probability, Institute of Mathematical Statistics, 2021, 49 (2), pp.944-996. ⟨10.1214/20-AOP1465⟩. ⟨hal-02339372⟩

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