Abstract
To characterize the regularity of nonlinear Fokker-Planck equations with respect to weighted variational distances, we establish for the first time a Bismut type formula for the extrinsic derivative of distribution dependent SDEs (DDSDEs). As an application, the Lipschitz continuity in the weighted variational distance is derived for the associated nonlinear Fokker-Planck equation, which can be regarded as the counterpart of the classical contraction property in the linear setting. The main results are illustrated by non-degenerate DDSDEs with space-time singular drift, as well as degenerate DDSDEs with weakly monotone coefficients. © 2025 ISI/BS.
| Original language | English |
|---|---|
| Pages (from-to) | 2508-2524 |
| Journal | Bernoulli |
| Volume | 31 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Aug 2025 |
Funding
The author is supported by NNSFC (12301180) and Research Centre for Nonlinear Analysis at Hong Kong PolyU.
Research Keywords
- Bismut formula
- distribution dependent SDEs
- extrinsic formula
- stochastic Hamiltonian system