Nonlocal elliptic equation in Holder space and the martingale problem

被引：6

作者：

Ling, Chengcheng ^{[1
]}

Zhao, Guohuan ^{[1
]}

机构：

[1] Bielefeld Univ, Fac Math, D-33615 Bielefeld, Germany

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 314卷

关键词：

Nonlocal equation; L?vy process; Martingale problem; Besov space; Fokker Planck equation; STOCHASTIC DIFFERENTIAL-EQUATIONS; UNIQUENESS; EXISTENCE; DRIVEN; SDES;

D O I：

10.1016/j.jde.2022.01.025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The well-posedness of nonlocal elliptic equation with singular drift is investigated in Besov-Holder spaces. As an application of our main analytic results, we show the existence and uniqueness for corresponding martingale problem. Moreover, we prove that the one dimensional distribution of the martingale solution has a density in certain Besov space.(c) 2022 Elsevier Inc. All rights reserved.

引用

页码：653 / 699

页数：47

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