Rough nonlocal diffusions
arXiv:1905.07270 · doi:10.1016/j.spa.2021.07.002
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.
55 pages. Corrected minor typos in version 2
References in corpus (6)
- Stochastic nonlinear Fokker-Planck equations
- Pathwise McKean-Vlasov Theory with Additive Noise
- Controlling Rough Paths
- Existence, uniqueness and stability of semi-linear rough partial differential equations
- Propagation of chaos for mean field rough differential equations
- Geometric rough paths on infinite dimensional spaces