Denker–Sato type Markov chains on self-similar sets
Publication in refereed journal

香港中文大學研究人員
替代計量分析
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其它資訊
摘要In Denker and Sato (Potential Anal 14: 211–232, 2001; Publ RIMS 35: 769–794, 1999; Math Nachr 241: 32–55, 2002) studied certain Markov chain on the symbolic spaces of the Sierpinski gasket (SG). They showed that the Martin boundary is homeomorphic to SG, and used the potential theory on the Martin boundary to induce a harmonic structure on SG. In this paper, we consider a more general Denker–Sato type Markov chain associated with self-similar sets $$K$$K with the open set condition. The chain is defined on the augmented tree of the symbolic space. Such tree was introduced by Kaimanovich, it is hyperbolic in the sense of Gromov (Kaimanovich in Random walks on Sierpiński graphs: hyperbolicity and stochastic homogenization, Birha̋user, Basel, 2003; Lau and Wang in Indiana Univ Math J 58:1777–1795, 2009). We show that the Martin boundary, the hyperbolic boundary and the self-similar set $$K$$K are homeomorphic. The hitting distribution of the chain is also obtained.
著者Lau K.-S., Wang X.-Y.
期刊名稱Mathematische Zeitschrift
出版年份2015
月份6
日期1
卷號280
期次1-2
出版社Springer Verlag
出版地Germany
頁次401 - 420
國際標準期刊號0025-5874
電子國際標準期刊號1432-1823
語言英式英語
關鍵詞Harmonic functions, Hyperbolic boundary, Iterated function system, Markov chain, Martin boundary, Self-similar sets

上次更新時間 2021-28-02 於 01:43