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.

中文翻译：

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粗略的非局部扩散

我们考虑由确定性粗糙路径驱动的非线性 Fokker-Planck 方程，该路径描述具有“共同”噪声的 McKean-Vlasov 扩散的条件概率。为了研究方程，我们建立了一个独立的非线性粗糙积分理论框架，我们用它来研究受粗糙路径扰动的 McKean-Vlasov 方程。我们构建了相应 Fokker-Planck 方程的解的适当概念并证明了适定性。