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

页码：125 / 163

页数：39

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