Back to Search
Start Over
Nonlocal, nonlinear Fokker-Planck equations and nonlinear martingale problems
- Publication Year :
- 2023
-
Abstract
- This work is concerned with the existence of mild solutions and the uniqueness of distributional solutions to nonlinear Fokker-Planck equations with nonlocal operators $\Psi(-\Delta)$, where $\Psi$ is a Bernstein function. As applications, the existence and uniqueness of solutions to the corresponding nonlinear martingale problems are proved. Furthermore, it is shown that these solutions form a nonlinear Markov process in the sense of McKean such that their one-dimensional time marginal law densities are the solutions to the nonlocal nonlinear Fokker-Planck equation. Hence, McKean's program envisioned in his PNAS paper from 1966 is realized for these nonlocal PDEs.<br />Comment: arXiv admin note: text overlap with arXiv:2210.05612
- Subjects :
- Mathematics - Analysis of PDEs
Mathematics - Probability
60H15, 47H05, 47J05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2308.06388
- Document Type :
- Working Paper