Solving mean field rough differential equations
Abstract
We provide in this work a robust solution theory for random rough differential equations of mean field type dXt = V(Xt,L(Xt))dt + F(Xt,L(Xt))dWt, where W is a random rough path and L(Xt) stands for the law of Xt, with mean field interaction in both the drift and diffusivity. The analysis 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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