Seminar Event Detail

Financial/Actuarial Mathematics

Date:  Tuesday, December 05, 2017
Location:  4096 East Hall (4:00 PM to 5:00 PM)

Title:  Mean field rough differential equations

Abstract: We provide in this work a robust solution theory for random rough differential equations of mean field type
dz_t = V\big(z_t,\cL(z_t)\big) + \textrm{F}\bigl( z_t,\cL(z_t)\bigr) dW_t,
where $W$ is a random rough path and $\cL(z_t)$ stands for the law of $z_t$, 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. 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.

Joint work with Remi Catellier (Nice) and Ismael Bailleul (Rennes)

Files: 4687_SemAnnArbor.pdf

Speaker:  Francois Delarue
Institution:  Universite Nice-Sophia Antipolis

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