On harmonic functions of symmetric Levy processes

被引：9

作者：

Mimica, Ante ^{[1
]}

机构：

[1] Univ Bielefeld, Fak Math, D-33615 Bielefeld, Nrw, Germany

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2014年 / 50卷 / 01期

关键词：

Geometric stable process; Green function; Harmonic function; Levy process; Modulus of continuity; Subordinator; Subordinate Brownian motion; HARNACK INEQUALITY; JUMP-PROCESSES; STABLE PROCESSES; POTENTIAL-THEORY; REGULARITY;

D O I：

10.1214/12-AIHP508

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider some classes of Levy processes for which the estimate of Krylov and Safonov (as in (Potential Anal. 17 (2002) 375-388)) fails and thus it is not possible to use the standard iteration technique to obtain a-priori Holder continuity estimates of harmonic functions. Despite the failure of this method, we obtain some a-priori regularity estimates of harmonic functions for these processes. Moreover, we extend results from (Probab. Theory Related Fields 135 (2006) 547-575) and obtain asymptotic behavior of the Green function and the Levy density for a large class of subordinate Brownian motions, where the Laplace exponent of the corresponding subordinator is a slowly varying function.

引用

页码：214 / 235

页数：22

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