Rough nonlocal diffusions

Michele Coghi and Torstein Nilssen

Stochastic Processes and their Applications, 2021, vol. 141, issue C, 1-56

Abstract: 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.

Keywords: Rough paths; Stochastic PDEs; McKean–Vlasov; Non-local equations (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2021.07.002

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