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Mean field rough differential equations

Abstract : We provide in this work a robust solution theory for random rough differential equations of mean field type driven by a random rough path, with mean field interaction in both the drift and diffusivity. Propagation of chaos results for large systems of interacting rough differential equations are obtained as a consequence, with explicit optimal convergence rate. The development of these results requires the introduction of a new rough path-like setting and an associated notion of controlled path. We use crucially Lions' approach to differential calculus on Wasserstein space along the way.
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Submitted on : Friday, February 16, 2018 - 7:20:55 PM
Last modification on : Thursday, January 20, 2022 - 9:02:01 AM
Long-term archiving on: : Monday, May 7, 2018 - 8:34:45 PM


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  • HAL Id : hal-01711183, version 1


Ismaël Bailleul, Rémi Catellier, Francois Delarue. Mean field rough differential equations. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2020. ⟨hal-01711183⟩



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