WIAS Preprint No. 2619, (2019)

Rough nonlocal diffusions



Authors

  • Coghi, Michele
    ORCID: 0000-0002-4198-0856
  • Nilssen, Torstein

2010 Mathematics Subject Classification

  • 60H05 60H15 35K55

Keywords

  • Rough paths, stochastic PDEs, McKean-Vlasov, non-local equations

DOI

10.20347/WIAS.PREPRINT.2619

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.

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