Rough nonlocal diffusions
- Coghi, Michele
- Nilssen, Torstein
2010 Mathematics Subject Classification
- 60H05 60H15 35K55
- Rough paths, stochastic PDEs, McKean-Vlasov, non-local equations
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.
- Stochastic Process. Appl., 141 (2021), pp. 1--56, DOI 10.1016/j.spa.2021.07.002 .