Infinite block-structured transition matrices and their properties
Zhao, YQQ; Li, W; Braun, WJ
AbstractIn this paper, we study Markov chains with infinite state block-structured transition matrices, whose states are partitioned into levels according to the block structure, and various associated measures. Roughly speaking, these measures involve first passage times or expected numbers of visits to certain levels without hitting other levels. They are very important and often play a key role in the study of a Markov chain. Necessary and/or sufficient conditions are obtained for a Markov chain to be positive recurrent, recurrent, or transient in terms of these measures. Results are obtained for general irreducible Markov chains as well as those with transition matrices possessing some block structure. We also discuss the decomposition or the factorization of the characteristic equations of these measures. In the scalar case, we locate the zeros of these characteristic functions and therefore use these zeros to characterize a Markov chain. Examples and various remarks are given to illustrate some of the results.
Keywordinfinite-state Markov chains block-form matrices Markov chains with repeating rows transient, recurrent and positive recurrent states censored Markov chains factorization of generating functions
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000075231600007
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Cited Times:19[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Affiliation1.Univ Winnipeg, Dept Math & Stat, Winnipeg, MB R3B 2E9, Canada
2.Chinese Acad Sci, Inst Appl Math, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Zhao, YQQ,Li, W,Braun, WJ. Infinite block-structured transition matrices and their properties[J]. ADVANCES IN APPLIED PROBABILITY,1998,30(2):365-384.
APA Zhao, YQQ,Li, W,&Braun, WJ.(1998).Infinite block-structured transition matrices and their properties.ADVANCES IN APPLIED PROBABILITY,30(2),365-384.
MLA Zhao, YQQ,et al."Infinite block-structured transition matrices and their properties".ADVANCES IN APPLIED PROBABILITY 30.2(1998):365-384.
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