Regularity of Harmonic functions for a class of singular stable-like processes

被引：29

作者：

Bass, Richard F. ^{[2
]}

Chen, Zhen-Qing ^{[1
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

MATHEMATISCHE ZEITSCHRIFT | 2010年 / 266卷 / 03期

基金：

美国国家科学基金会;

关键词：

Stable-like process; Pseudo-differential operator; Harmonic function; Holder continuity; Support theorem; Krylov-Safonov technique; Harnack inequality;

D O I：

10.1007/s00209-009-0581-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the system of stochastic differential equations dX(t)=A(X(t-))dZ(t), where Z(t)(1) , ... , Z(d)(t) are independent one-dimensional symmetric stable processes of order alpha, and the matrix-valued function A is bounded, continuous and everywhere non-degenerate. We show that bounded harmonic functions associated with X are Holder continuous, but a Harnack inequality need not hold. The Levy measure associated with the vector-valued process Z is highly singular.

引用

页码：489 / 503

页数：15

共 7 条

[1]

[Anonymous], 1983, ELLIPTIC PARTIAL DIF

[2]

[Anonymous], 1997, DIFFUSIONS ELLIPTIC

[3] Systems of equations driven by stable processes [J].