Rough mean field equations

18. January 2018
Research Seminars
Rudower Chaussee 25, Room 1.115, 5 p.m.
Francois Delarue (Université Nice-Sophia Antipolis)

We provide in this work a robust solution theory for random rough differential equations of mean field type

dX_t = V(X_t,L(X_t)) dt + F(X_t, L(X_t)) dW_t,
where W is a random rough path and L(X_t) stands for the law of X_t , 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 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. This is a joint work with I. Bailleul and R. Catellier.


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