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beta-invariant measures for transition matrices of GI/M/1 type
Li, QL; Zhao, YQ
AbstractIn this paper, we study transition matrices of GI/M/1 type by using the approach proposed in Li and Zhao.([13]) We obtain conditions on the a-classification of states for the transition matrix of GI/M/1 type. Unlike for matrices of M/G/1 type where association of the matrix multiplication can be easily justified, for matrices of GI/M/ type, we first construct formal expressions for the beta-invariant measure based on a representation of factorization of the transition matrix, and then show that it is a beta-invariant measure directly. We also prove some spectral properties for the matrix of GI/M/1 type, which are not only used in constructing a formal expression for the beta-invariant measure, but also of their own interest. We point out that the spectral analysis required for studying matrices of GI/M/1 type is much more sophisticated than that for matrices of M/G/1 type. Finally, we discuss connections of expressions for the,B-invariant measure provided in this paper and in the literature.
KeywordBeta-invariant Measures Quasi-stationary Distributions Markov Chains Of Gi/m/1 Type Radius Of Convergence The Rg-factorizations Spectral Analysis
WOS HeadingsScience & Technology ; Physical Sciences
Indexed BySCI
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000183261400002
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Cited Times:18[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Affiliation1.Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada
2.Chinese Acad Sci, Inst Automat, Natl Lab Pattern Recognit, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Li, QL,Zhao, YQ. beta-invariant measures for transition matrices of GI/M/1 type[J]. STOCHASTIC MODELS,2003,19(2):201-233.
APA Li, QL,&Zhao, YQ.(2003).beta-invariant measures for transition matrices of GI/M/1 type.STOCHASTIC MODELS,19(2),201-233.
MLA Li, QL,et al."beta-invariant measures for transition matrices of GI/M/1 type".STOCHASTIC MODELS 19.2(2003):201-233.
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