Difference between revisions of "Markov chain, periodic"
From Encyclopedia of Mathematics
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A non-decomposable homogeneous [[Markov chain|Markov chain]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m062/m062420/m0624201.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m062/m062420/m0624202.png" /> in which each state <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m062/m062420/m0624203.png" /> has period larger than 1, that is, | A non-decomposable homogeneous [[Markov chain|Markov chain]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m062/m062420/m0624201.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m062/m062420/m0624202.png" /> in which each state <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m062/m062420/m0624203.png" /> has period larger than 1, that is, | ||
Revision as of 20:24, 9 March 2012
2020 Mathematics Subject Classification: Primary: 60J10 [MSN][ZBL]
A non-decomposable homogeneous Markov chain 
, 
in which each state 
has period larger than 1, that is,
 |
In a non-decomposable Markov chain (cf. Markov chain, non-decomposable) all states have the same period. If 
, then the Markov chain is called aperiodic.
Comments
Cf. also Markov chain and Markov chain, decomposable for references.
How to Cite This Entry:
Markov chain, periodic. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Markov_chain,_periodic&oldid=11752
Markov chain, periodic. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Markov_chain,_periodic&oldid=11752
This article was adapted from an original article by V.P. Chistyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article