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.
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
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