Lineer Olmayan Kaba Fokker–Planck Denklemleri

Özet (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.

Yazarların özeti; kaynağından alınmıştır. Mathematical Physics Analysis and Geometry, 2026 · DOI ↗