Potential theory of truncated stable processes
Potential theory of truncated stable processes
复制标题
DOI：
10.1007/s00209-006-0063-6
复制
发表时间：
2006-05
影响因子：
0.8
通讯作者：
P. Kim;R. Song
中科院分区：
文献类型：
--
作者：
P. Kim;R. Song
对于任意的截断对称α-稳定过程，它是一个对称Lévy过程，对于某个常数，其Lévy密度由给出。本文详细研究了截断对称稳定过程的位势理论。我们证明了这些过程的非负调和函数的Harnack不等式。对于有界凸域上关于这些过程的调和函数，我们也建立了一个边界Harnack原理。我们给出了一个例子，一个非凸域的边界Harnack原则失败。
For any, a truncated symmetric α-stable process is a symmetric Lévy process inwith a Lévy density given byfor some constantc. In this paper we study the potential theory of truncated symmetric stable processes in detail. We prove a Harnack inequality for nonnegative harmonic functions of these processes. We also establish a boundary Harnack principle for nonnegative functions which are harmonic with respect to these processes in bounded convex domains. We give an example of a non-convex domain for which the boundary Harnack principle fails.