Geodesic
On dependence structure of copula-based Markov chains
ESAIM: Probability and Statistics, Tome 18 (2014), pp. 570-583

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We consider dependence coefficients for stationary Markov chains. We emphasize on some equivalencies for reversible Markov chains. We improve some known results and provide a necessary condition for Markov chains based on Archimedean copulas to be exponential ρ-mixing. We analyse the example of the Mardia and Frechet copula families using small sets.

DOI : 10.1051/ps/2013052
Classification : 60J20, 60J35, 37A30
Keywords: Markov chains, copula, mixing, reversible processes, ergodicity, small sets 
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     author = {Longla, Martial},
     title = {On dependence structure of copula-based {Markov} chains},
     journal = {ESAIM: Probability and Statistics},
     pages = {570--583},
     publisher = {EDP-Sciences},
     volume = {18},
     year = {2014},
     doi = {10.1051/ps/2013052},
     zbl = {1308.60087},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2013052/}
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Longla, Martial. On dependence structure of copula-based Markov chains. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 570-583. doi: 10.1051/ps/2013052

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