Quantitative stability estimates for Fokker-Planck equations

被引：6
作者：
Li, Huaiqian [1 ]
Luo, Dejun [2 ,3 ]
机构：
[1] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China
[2] Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Random Complex Struct & Data Sci, Beijing 100190, Peoples R China
[3] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
来源：
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2019年 / 122卷
基金：
中国国家自然科学基金;
关键词：
Fokker-Planck equation; Stability estimate; Kantorovich-Rubinstein distance; Superposition principle; DIFFERENTIAL-EQUATIONS; SOBOLEV DIFFUSION; TRANSPORT-EQUATION; WELL-POSEDNESS; CAUCHY-PROBLEM; SDES; UNIQUENESS; DEGENERATE; EXISTENCE; DRIFT;
D O I：
10.1016/j.matpur.2018.08.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We derive quantitative stability estimates for solutions of Fokker-Planck equations with irregular coefficients. We are mainly concerned with two different situations: in the degenerate case, the coefficients are assumed to be weakly differentiable, while in the non-degenerate case the drift coefficient satisfies only the Ladyzhenskaya- Prodi-Serrin condition. Our method is based on Trevisan's superposition principle, which represents the solution to the Fokker-Planck equation as the marginal distribution of the martingale solution of the associated stochastic differential equation. (C) 2018 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：125 / 163
页数：39
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