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Article Dans Une Revue Electronic Journal of Probability Année : 2020

Mean field rough differential equations

Résumé

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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Dates et versions

hal-01711183 , version 1 (16-02-2018)

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  • HAL Id : hal-01711183 , version 1

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Ismaël Bailleul, Rémi Catellier, Francois Delarue. Mean field rough differential equations. Electronic Journal of Probability, 2020. ⟨hal-01711183⟩
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