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تسجيل مستخدم جديدPropagation of chaos for mean field rough differential equations
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We address propagation of chaos for large systems of rough differential equations associated with random rough differential equations of mean field type $$ dX_t = V(X_t,mathcal{L}(X_t))dt + F(X_t,mathcal{L}(X_t))dW_t $$ where $W$ is a random rough path and $mathcal{L}(X_t)$ is the law of $X_t$. We prove propagation of chaos, and provide also an explicit optimal convergence rate. The analysis is based upon the tools we developed in our companion paper [1] for solving mean field rough differential equations and in particular upon a corresponding version of the It^o-Lyons continuity theorem. The rate of convergence is obtained by a coupling argument developed first by Sznitman for particle systems with Brownian inputs.
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