English

Rough nonlocal diffusions

Probability 2021-07-27 v2 Analysis of PDEs

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

Cite

@article{arxiv.1905.07270,
  title  = {Rough nonlocal diffusions},
  author = {Michele Coghi and Torstein Nilssen},
  journal= {arXiv preprint arXiv:1905.07270},
  year   = {2021}
}

Comments

55 pages. Corrected minor typos in version 2