A NEW APPROACH TO COMPUTING THE TRANSIENT-STATE PROBABILITIES IN TIME-INHOMOGENEOUS MARKOV CHAINS
A NEW APPROACH TO COMPUTING THE TRANSIENT-STATE PROBABILITIES IN TIME-INHOMOGENEOUS MARKOV CHAINS
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DOI：
10.15807/jorsj.65.48
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发表时间：
2022-01
影响因子：
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通讯作者：
Yoshiaki Inoue
中科院分区：
文献类型：
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作者：
Yoshiaki Inoue
本文研究了非齐次连续时间马氏链的暂态概率的计算问题。我们首先引入了一类新的时间非齐次马氏链，它与非负概率分布的相型表示密切相关。fi首次提出了一类新的非齐次马氏链。我们证明了引入的马氏链覆盖了一大类非齐次马氏链。在此基础上，给出了这类马氏链的暂态概率的一种计算方法，该方法是时齐马氏链中的统一化方法的推广。与文献中已知的方法不同，该方法具有一个显著的特点，即不需要对生成器进行时间离散化。
This paper considers the computation of the transient-state probabilities in time-inhomogenous continuous-time Markov chains. We first introduce a new class of time-inhomogenous Markov chains, which is closely related to the phase-type representation of non-negative probability distributions. We show that the introduced class of Markov chains covers a wide-class of time-inhomogenous Markov chains. We then develop a computational method of the transient-state probabilities in Markov chains of this class, which is an extension of the uniformization method in time-homogeneous Markov chains. The developed computational method has a remarkable feature that the time-discretization of the generator is not necessary, as opposed to previously known methods in the literature.