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Statistical Identification of Markov Chain on Trees

机译：树上马尔可夫链的统计辨识

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摘要

The theoretical study of continuous-time homogeneous Markov chains is usually based on a natural assumption of a known transition rate matrix (TRM). However, the TRM of a Markov chain in realistic systems might be unknown and might even need to be identified by partially observable data. Thus, an issue on how to identify the TRM of the underlying Markov chain by partially observable information is derived from the great significance in applications. That is what we call the statistical identification of Markov chain. The Markov chain inversion approach has been derived for basic Markov chains by partial observation at few states. In the current letter, a more extensive class of Markov chain on trees is investigated. Firstly, a type of a more operable derivative constraint is developed. Then, it is shown that all Markov chains on trees can be identified only by such derivative constraints of univariate distributions of sojourn time and/or hitting time at a few states. A numerical example is included to demonstrate the correctness of the proposed algorithms.
机译：连续时间齐次马尔可夫链的理论研究通常基于已知跃迁速率矩阵（TRM）的自然假设。但是，现实系统中的马尔可夫链的TRM可能是未知的，甚至可能需要通过部分可观察的数据来识别。因此，关于如何通过部分可观察的信息来识别基础马尔可夫链的TRM的问题，从应用中具有重要意义。这就是我们所说的马尔可夫链的统计识别。马尔可夫链反演方法是通过在少数几个州进行局部观察得出的，用于基本马尔可夫链。在当前的信中，对树上的马尔可夫链进行了更广泛的研究。首先，开发了一种更可操作的导数约束。然后，表明仅通过在几个状态下停留时间和/或命中时间的单变量分布的这种导数约束，才能识别树上的所有马尔可夫链。包括一个数值示例，以证明所提出算法的正确性。

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  • 来源
    《Mathematical Problems in Engineering》 |2018年第3期|2036248.1-2036248.13|共13页
  • 作者

    Xiang Xuyan; Zhang Xiao; Mo Xiaoyun;

  • 作者单位

    Hunan Univ Arts & Sci, Sch Math & Computat Sci, Hunan Prov Cooperat Innovat Ctr Construct & Dev D, Changde 415000, Peoples R China;

    Jishou Univ, Sch Math & Stat, Jishou 416000, Peoples R China;

    Hunan Univ Finance & Econ, Sch Math & Stat, Changsha 410205, Hunan, Peoples R China;

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