On weak lumpability of a finite Markov chain

NanFu Peng

doi:10.1016/0167-7152(95)00091-7

On weak lumpability of a finite Markov chain

NanFu Peng^*

^*Corresponding author for this work

Institute of Statistics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

An irreducible and homogeneous Markov chain with finite state space is considered. Under a mild condition Γ on the transition probability matrix, a necessary and sufficient condition for weak lumpability, and the characterization of the set of initial starting vectors which make it lumpable are obtained. A similar result is obtained for those transition probability matrices without the restriction of condition Γ.

Original language	English
Pages (from-to)	313-318
Number of pages	6
Journal	Statistics and Probability Letters
Volume	27
Issue number	4
DOIs	https://doi.org/10.1016/0167-7152(95)00091-7
State	Published - 1 May 1996

Keywords

Markov chain
Weak lumpability

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10.1016/0167-7152(95)00091-7

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abstract = "An irreducible and homogeneous Markov chain with finite state space is considered. Under a mild condition Γ on the transition probability matrix, a necessary and sufficient condition for weak lumpability, and the characterization of the set of initial starting vectors which make it lumpable are obtained. A similar result is obtained for those transition probability matrices without the restriction of condition Γ.",

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AU - Peng, NanFu

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N2 - An irreducible and homogeneous Markov chain with finite state space is considered. Under a mild condition Γ on the transition probability matrix, a necessary and sufficient condition for weak lumpability, and the characterization of the set of initial starting vectors which make it lumpable are obtained. A similar result is obtained for those transition probability matrices without the restriction of condition Γ.

AB - An irreducible and homogeneous Markov chain with finite state space is considered. Under a mild condition Γ on the transition probability matrix, a necessary and sufficient condition for weak lumpability, and the characterization of the set of initial starting vectors which make it lumpable are obtained. A similar result is obtained for those transition probability matrices without the restriction of condition Γ.

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KW - Weak lumpability

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U2 - 10.1016/0167-7152(95)00091-7

DO - 10.1016/0167-7152(95)00091-7

M3 - Article

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VL - 27

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EP - 318

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 4

ER -

On weak lumpability of a finite Markov chain

Abstract

Keywords

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