Infinite block-structured transition matrices and their properties

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	Infinite block-structured transition matrices and their properties
	Zhao, YQQ ; Li, W ; Braun, WJ
	1998-06-01
发表期刊	ADVANCES IN APPLIED PROBABILITY
ISSN	0001-8678
卷号	30 期号:2 页码:365-384
摘要	In 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.
关键词	infinite-state Markov chains block-form matrices Markov chains with repeating rows transient, recurrent and positive recurrent states censored Markov chains factorization of generating functions
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000075231600007
出版者	APPLIED PROBABILITY TRUST
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13971
专题	中国科学院数学与系统科学研究院
通讯作者	Zhao, YQQ
作者单位	1.Univ Winnipeg, Dept Math & Stat, Winnipeg, MB R3B 2E9, Canada 2.Chinese Acad Sci, Inst Appl Math, Beijing, Peoples R China
推荐引用方式 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.