Sierpiński垫圈作为非各向同性Markov链的Martin边界

IF 0.7 4区数学 Q1 MATHEMATICS Journal of Fractal Geometry Pub Date : 2017-10-12 DOI:10.4171/JFG/86

Marc Kessebohmer, Tony Samuel, K. Sender

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引用次数: 2

摘要

2012年，在Denker和Sato工作的推动下，Lau和Ngai给出了一个三字母字母表上有限词集上的各向同性马尔可夫链的例子，其Martin边界与Sierpinski垫圈同胚。在这里，我们将Lau和Ngai的结果推广到一类非各向同性马尔可夫链。我们确定了Martin边界，并证明了最小Martin边界是Martin边界的一个子集。此外，我们还描述了调和函数的集合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain

In 2012 Lau and Ngai, motivated by the work of Denker and Sato, gave an example of an isotropic Markov chain on the set of finite words over a three letter alphabet, whose Martin boundary is homeomorphic to the Sierpinski gasket. Here, we extend the results of Lau and Ngai to a class of non-isotropic Markov chains. We determine the Martin boundary and show that the minimal Martin boundary is a proper subset of the Martin boundary. In addition, we give a description of the set of harmonic functions.

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