On the structure of 1-dependent Markov chains

Jon Aaronson; David Gilat; Michael Keane

doi:10.1007/BF01060435

On the structure of 1-dependent Markov chains

Jon Aaronson^*, David Gilat, Michael Keane

^*Corresponding author for this work

School of Mathematical Sciences

Delft University of Technology

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

16 Scopus citations

Abstract

Any stationary 1-dependent Markov chain with up to four states is a 2-block factor of independent, identically distributed random variables. There is a stationary 1-dependent Markov chain with five states which is not, even though every 1-dependent renewal process is a 2-block factor.

Original language	English
Pages (from-to)	545-561
Number of pages	17
Journal	Journal of Theoretical Probability
Volume	5
Issue number	3
DOIs	https://doi.org/10.1007/BF01060435
State	Published - Jul 1992

Keywords

1-dependence
Stationary Markov chain
block factor

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10.1007/BF01060435

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title = "On the structure of 1-dependent Markov chains",

abstract = "Any stationary 1-dependent Markov chain with up to four states is a 2-block factor of independent, identically distributed random variables. There is a stationary 1-dependent Markov chain with five states which is not, even though every 1-dependent renewal process is a 2-block factor.",

keywords = "1-dependence, Stationary Markov chain, block factor",

author = "Jon Aaronson and David Gilat and Michael Keane",

year = "1992",

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AU - Keane, Michael

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AB - Any stationary 1-dependent Markov chain with up to four states is a 2-block factor of independent, identically distributed random variables. There is a stationary 1-dependent Markov chain with five states which is not, even though every 1-dependent renewal process is a 2-block factor.

KW - 1-dependence

KW - Stationary Markov chain

KW - block factor

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JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

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On the structure of 1-dependent Markov chains

Abstract

Keywords

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