Mathematical Physics Analysis and Geometry· 2026Q2
Nonlinear Rough Fokker–Planck Equations
- 8citations
- Q2SCImago
- 2026year
Short summary
Rough path techniques enable well-posedness for nonlinear, nonlocal stochastic Fokker–Planck equations (SPDEs) without the dimension-dependent regularity assumptions previously required.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces rough path techniques to analyze nonlinear, nonlocal stochastic Fokker–Planck equations (SPDEs).
- Establishes well-posedness for these SPDEs without requiring dimension-dependent regularity assumptions on coefficients.
- Demonstrates that rough path methods impose fewer regularity demands than classical stochastic analysis approaches.
- These SPDEs are key components in mean-field games with common noise.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract McKean–Vlasov SDEs describe systems where the dynamics depend on the law of the process. The corresponding Fokker–Planck equation is a nonlinear, nonlocal PDE for the corresponding measure flow. In the presence of common noise and conditional law dependence, the evolution becomes random and is governed by a stochastic Fokker–Planck equation; that is, a nonlinear, nonlocal SPDE in the space of measures. (Such equations constitute an important ingredient in the theory of mean-field games with common noise.) Well-posedness of such SPDEs is a difficult problem, the best result to date due to Coghi–Gess [5], which however comes with dimension-dependent regularity assumptions. In the present work, we show how rough path techniques can circumvent these entirely. Hence, and somewhat contrarily to common belief, the use of rough paths leads to substantially less regularity demands on the coefficients than methods rooted in classical stochastic analysis methods.
The authors' abstract, as published at the source. Mathematical Physics Analysis and Geometry, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Finance
FinanceEconomics, Econometrics and Finance