Geodesic
On Series of $H$-Equivalent Tuples in Markov Chains
Informatics and Automation, Branching Processes and Related Topics, Tome 316 (2022), pp. 270-284

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Let $\mathbf {X}=(X_0,X_1,\ldots )$ be an irreducible Markov chain with state set $\{1,\ldots ,N\}$ and $H$ be a permutation group on the set $\{1,\ldots ,N\}$. We prove limit theorems for the number of series of $H$-equivalent $s$-tuples that start before time $n$ inclusive. These results continue the series of our works within the research direction initiated in the 1970s by A. M. Zubkov and other authors.
Mots-clés : Markov chain, $H$-equivalent tuples, Poisson limit theorem. 
@article{TRSPY_2022_316_a17,
     author = {V. G. Mikhailov and A. M. Shoitov and A. V. Volgin},
     title = {On {Series} of $H${-Equivalent} {Tuples} in {Markov} {Chains}},
     journal = {Informatics and Automation},
     pages = {270--284},
     publisher = {mathdoc},
     volume = {316},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2022_316_a17/}
}
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V. G. Mikhailov; A. M. Shoitov; A. V. Volgin. On Series of $H$-Equivalent Tuples in Markov Chains. Informatics and Automation, Branching Processes and Related Topics, Tome 316 (2022), pp. 270-284. http://geodesic.mathdoc.fr/item/TRSPY_2022_316_a17/