Identifying Q-Matrix of Cyclic Markov Chain

Xu Yan XIANG, Xiang Qun YANG, Ying Chun DENG

Acta Mathematica Sinica, Chinese Series ›› 2013, Vol. 56 ›› Issue (5) : 735-750.

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Acta Mathematica Sinica, Chinese Series ›› 2013, Vol. 56 ›› Issue (5) : 735-750. DOI: 10.12386/A2013sxxb0073
Articles

Identifying Q-Matrix of Cyclic Markov Chain

  • Xu Yan XIANG1, Xiang Qun YANG2, Ying Chun DENG2
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Abstract

The sojourn time and hitting time distributions (the mixtures of exponential distributions) are provided for a given subset of state space of Markov chain. Then the derivatives of these distributions at t=0 are related to the Q-matrix. Based on the constraint relationships and the priori information from the structure of Markov chain, an inversion approach is developed to identify the transition rates from the parameters characterizing these distributions. For cyclic Markov chain with finite states, as a result, it is derived that its Q-matrix can be uniquely determined by the distributions of their sojourn time and hitting time at arbitrary two adjacent states. The corresponding algorithm is included to show the validity of such approach.

Key words

Markov chain / cyclic scheme / reversibility / transition rate / sojourn time / hitting time

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Xu Yan XIANG, Xiang Qun YANG, Ying Chun DENG. Identifying Q-Matrix of Cyclic Markov Chain. Acta Mathematica Sinica, Chinese Series, 2013, 56(5): 735-750 https://doi.org/10.12386/A2013sxxb0073

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