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