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On Series of \(H\)-Equivalent Tuples in Markov Chains

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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.

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Acknowledgments

We are grateful to the referee for useful remarks that helped us to improve the statements of the theorems and eliminate numerous typing misprints in the manuscript.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    V. G. Mikhailov

  2. Academy of Cryptography of the Russian Federation, ul. Yartsevskaya 30, Moscow, 121552, Russia

    A. M. Shoitov

  3. MIREA – Russian Technological University, prosp. Vernadskogo 78, Moscow, 119454, Russia

    A. V. Volgin

Authors
  1. V. G. Mikhailov
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  2. A. M. Shoitov
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  3. A. V. Volgin
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Correspondence to V. G. Mikhailov.

Additional information

Translated from Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Vol. 316, pp. 270–284 https://doi.org/10.4213/tm4204.

Translated by I. Nikitin

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Mikhailov, V.G., Shoitov, A.M. & Volgin, A.V. On Series of \(H\)-Equivalent Tuples in Markov Chains. Proc. Steklov Inst. Math. 316, 254–267 (2022). https://doi.org/10.1134/S0081543822010187

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  • DOI: https://doi.org/10.1134/S0081543822010187

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