Boundary Harnack inequality for Markov processes with jumps
Boundary Harnack inequality for Markov processes with jumps
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带跳跃的马尔可夫过程的边界 Harnack 不等式
DOI：
10.1090/s0002-9947-2014-06127-8
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
T. Kumagai and M. Kwaśnicki
中科院分区：
文献类型：
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作者：
K. Bogdan;T. Kumagai and M. Kwaśnicki
在跳核的相似性估计和跳过程生成元的Urysohn型性质的相似性估计下，证明了度量测度状态空间上跳型Markov过程的边界Harnack不等式.这一结果对任意开集上的正调和函数都成立。它适用于，例如，许多下属布朗运动，列维过程，并没有连续的一部分，稳定和审查稳定的过程，跳跃过程的分形，而一般薛定谔，漂移和跳跃扰动等过程。引用
We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process. The result holds for positive harmonic functions in arbitrary open sets. It applies, eg, to many subordinate Brownian motions, Lévy processes with and without continuous part, stable-like and censored stable processes, jump processes on fractals, and rather general Schrödinger, drift and jump perturbations of such processes. References