Flux and Lateral Conditions for Symmetric Markov Processes
Flux and Lateral Conditions for Symmetric Markov Processes
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DOI：
10.1007/s11118-008-9097-1
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发表时间：
2008-09
影响因子：
1.1
通讯作者：
Zhen-Qing Chen;M. Fukushima
中科院分区：
文献类型：
--
作者：
Zhen-Qing Chen;M. Fukushima
本文的目的是在无穷小发生器水平上对40多年来存在的具有一般拟闭边界的对称马尔可夫过程的Feller边界问题给出一个肯定的答案。为此，我们引入了通量泛函的新概念，它可以通过内部的最小过程来定义。然后，我们用它来表征扩展x0的对称过程的2无穷小生成器。特别要注意的是，当边界由可计数的多个点组成时，这些点没有累积点。
The purpose of this paper is to give an affirmative answer at infinitesimal generator level to the 40 years old Feller’s boundary problem for symmetric Markov processes with general quasi-closed boundaries. For this, we introduce a new notion of flux functional, which can be intrinsically defined via the minimal processX0in the interior. We then use it to characterize theL2-infinitesimal generator of a symmetric process that extendsX0. Special attention is paid to the case when the boundary consists of countable many points possessing no accumulation points.