Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (6): 1682-1698.

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Statistical Identification of Reversible Markov Chain on Cyclic Graph

Xuyan Xiang1,*(),Haiqin Fu2,Jieming Zhou3,Yingchun Deng3,Xiangqun Yang3   

  1. 1 Hunan Province Cooperative Innovation Center for The Construction and Development of Dongting Lake Ecological Economic Zone & School of Mathematics and Physics, Hunan University of Arts and Science, Hunan Changde 415000
    2 School of Mathematics and Computational Science, Xiangtan University, Hunan Xiangtan 411105
    3 LCSM, Ministry of Education, School of Mathematics and Statistics, Hunan Normal University, Changsha 410081
  • Received:2020-03-08 Online:2020-12-26 Published:2020-12-29
  • Contact: Xuyan Xiang
  • Supported by:
    the NSFC(11671132);the Key Scientific Research Project of Hunan Provincial Education Department(19A342);the Applied Economics of Hunan Province


The statistical identification of Markov chain explores how to identify the transition rate matrix of the underlying Markov chain by partially observable data. SIMC on reversibly cyclic graphs (containing one cycle at least), as the most important and crucial class, is investigated then in this letter. As the differentials of hitting time distribution for a reversible Markov chain are expressed by taboo rates, the necessary condition is developed to identify the transition rate matrix and a general conclusion about sufficiency is provided. The proposed algorithms to exactly calculate all transition rates are developed. A numerical example is included to demonstrate the correctness of the proposed algorithms.

Key words: Reversible Markov chain, Transition rate matrix, Statistical identification, Cyclic graph, Hitting time

CLC Number: 

  • O211.62