Hypoellipticity and Parabolic Hypoellipticity of Nonlocal Operators under Hormander's Condition

被引：1

作者：

Ren, Jiagang ^{[1
]}

Zhang, Hua ^{[2
]}

机构：

[1] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Guangdong, Peoples R China

[2] Jiangxi Univ Finance & Econ, Sch Stat, Nanchang 330013, Jiangxi, Peoples R China

来源：

POTENTIAL ANALYSIS | 2023年 / 59卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Hypoellipticity; Parabolic hypoellipticity; Hormander's condition; Stochastic differential equations; Multiplicative Levy noises; Poisson functional; Dirichlet form; Gradient; Carre du champ; FUNDAMENTAL-SOLUTIONS; SMOOTH DENSITIES; JUMPS; EXISTENCE; SDES;

D O I：

10.1007/s11118-022-09997-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove the hypoellipticity and parabolic hypoellipticity of nonlocal operators under Hormander's condition. One key step in the proof is to obtain an off-diagonal small time estimate of the densities of the processes associated to these operators. To this end, we use a new version of Malliavin calculus on the Poisson space, namely the lent particle method, recently developed by Bouleau and Denis.

引用

页码：1051 / 1078

页数：28

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