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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 316, Pages 270–284
DOI: https://doi.org/10.4213/tm4204 (Mi tm4204) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On Series of $H$-Equivalent Tuples in Markov Chains

V. G. Mikhailova, A. M. Shoitovb, A. V. Volginc

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Academy of Cryptography of the Russian Federation, ul. Yartsevskaya 30, Moscow, 121552 Russia
c MIREA – Russian Technological University, prosp. Vernadskogo 78, Moscow, 119454 Russia
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DOI: https://doi.org/10.4213/tm4204
Abstract: 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.
Keywords: Markov chain, $H$-equivalent tuples, Poisson limit theorem.
Received: March 18, 2021
Revised: April 11, 2021
Accepted: June 24, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 316, Pages 254–267
DOI: https://doi.org/10.1134/S0081543822010187
Bibliographic databases:
Document Type: Article
UDC: 519.212.2
Language: Russian
Citation: V. G. Mikhailov, A. M. Shoitov, A. V. Volgin, “On Series of $H$-Equivalent Tuples in Markov Chains”, Branching Processes and Related Topics, Collected papers. On the occasion of the 75th birthday of Andrei Mikhailovich Zubkov and 70th birthday of Vladimir Alekseevich Vatutin, Trudy Mat. Inst. Steklova, 316, Steklov Math. Inst., Moscow, 2022, 270–284; Proc. Steklov Inst. Math., 316 (2022), 254–267
Citation in format AMSBIB
\Bibitem{MikShoVol22}
\by V.~G.~Mikhailov, A.~M.~Shoitov, A.~V.~Volgin
\paper On Series of $H$-Equivalent Tuples in Markov Chains
\inbook Branching Processes and Related Topics
\bookinfo Collected papers. On the occasion of the 75th birthday of Andrei Mikhailovich Zubkov and 70th birthday of Vladimir Alekseevich Vatutin
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 316
\pages 270--284
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4204}
\crossref{https://doi.org/10.4213/tm4204}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 316
\pages 254--267
\crossref{https://doi.org/10.1134/S0081543822010187}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129149490}
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    • This publication is cited in the following 1 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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