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Rough nonlocal diffusions

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  • Coghi, Michele
  • Nilssen, Torstein

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.

Suggested Citation

  • Coghi, Michele & Nilssen, Torstein, 2021. "Rough nonlocal diffusions," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 1-56.
    • Handle: RePEc:eee:spapps:v:141:y:2021:i:c:p:1-56
    DOI: 10.1016/j.spa.2021.07.002
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    References listed on IDEAS

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    1. Kurtz, Thomas G. & Xiong, Jie, 1999. "Particle representations for a class of nonlinear SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 103-126, September.
    2. Diehl, Joscha & Oberhauser, Harald & Riedel, Sebastian, 2015. "A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 161-181.
    3. Deya, Aurélien & Gubinelli, Massimiliano & Hofmanová, Martina & Tindel, Samy, 2019. "One-dimensional reflected rough differential equations," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3261-3281.
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    Cited by:

    1. Harang, Fabian A. & Mayorcas, Avi, 2023. "Pathwise regularisation of singular interacting particle systems and their mean field limits," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 499-540.

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