在R上取值树指标马氏链的等价性质

丁承军, 景颖, 杨卫国

数学学报 ›› 2023, Vol. 66 ›› Issue (1) : 143-148.

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PDF(323 KB)
数学学报 ›› 2023, Vol. 66 ›› Issue (1) : 143-148. DOI: 10.12386/A20210010
论文

在R上取值树指标马氏链的等价性质

    丁承军, 景颖, 杨卫国
作者信息 +

The Equivalent Properties of Markov Chains Indexed by a Tree Taking Value on R

    Cheng Jun DING, Ying JING, Wei Guo YANG
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文章历史 +

摘要

本文参照Benjamini和Peres的离散状态树指标马氏链的定义,给出在R上取值树指标马氏链的定义, 并给出其若干等价性质.

Abstract

In the paper, we give the definition of the Markov chains indexed by a tree taking value on R. Then, we prove the equivalent properties of it.

关键词

马氏链 / / 等价性质

Key words

Makov chains / tree / equivalent property

引用本文

导出引用
丁承军, 景颖, 杨卫国. 在R上取值树指标马氏链的等价性质. 数学学报, 2023, 66(1): 143-148 https://doi.org/10.12386/A20210010
Cheng Jun DING, Ying JING, Wei Guo YANG. The Equivalent Properties of Markov Chains Indexed by a Tree Taking Value on R. Acta Mathematica Sinica, Chinese Series, 2023, 66(1): 143-148 https://doi.org/10.12386/A20210010

参考文献

[1] Benjamini I., Peres Y., Markov chains indexed by trees, Ann. Probab., 1994, 22:219-243.
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[7] Yang W. G., Some limit properties for Markov chains indexed by a homogeneous tree, Statist. Probab. Lett., 2003, 65(3):241-250.
[8] Yang W. G., Liu W., Strong law of large numbers for Markov chains field on a Bethe tree, Statist. Probab. Lett., 2000, 49(3):245-250.
[9] Yang W. G., Liu W., Strong law of large numbers and Shannon-McMillan theorem for Markov chain fields on trees, IEEE Trans. Inform. Theory, 2002, 48(1):311-318.

基金

国家自然科学基金资助项目(11571142);江苏高校优势学科建设工程(三期: PAPD-2018-87)
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