Date
Mon, 23 Apr 2018
Time
15:45 - 16:45
Location
L3
Speaker
FRANCOIS DELARUE
Organisation
University of Nice Sophia-Antipolis

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

$$

dX_t = V\big( X_t,{\mathcal L}(X_t)\big)dt + \textrm{F}\bigl( X_t,{\mathcal L}(X_t)\bigr) dW_t,

$$

where $W$ is a random rough path and ${\mathcal L}(X_t)$ 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.

Joint work with I. Bailleul (Rennes) and R. Catellier (Nice)

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