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Author: Coghi, Michele × Subject: stochastic PDEs ×

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    Rough nonlocal diffusions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Coghi, Michele; Nilssen, Torstein
    We consider a nonlinear Fokker-Planck equation driven by a deterministic rough path which describes the conditional probability of a McKean-Vlasov diffusion with "common" noise. To study the equation we build a self-contained framework of non-linear rough integration theory which we use to study McKean-Vlasov equations perturbed by rough paths. We construct an appropriate notion of solution of the corresponding Fokker-Planck equation and prove well-posedness.