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Zapiski Nauchnykh Seminarov POMI, 2023, Volume 524, Pages 7–17 (Mi znsl7352)  
Ergodicity index of the set of stochastic matrices

Yu. A. Al'pin, V. S. Al'pina

Kazan'
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Abstract: The paper introduces and explores the notions of ergodicity index and ergodicity exponent of a set of stochastic matrices. For the ergodicity exponent a sharp upper bound is obtained. A particular case of this bound is the well-known Paz bound. Also a connection between the ergodicity index and the Protasov–Voynov imprimitivity index is established.
Key words and phrases: stochastic matrix, imprimitivity index, ergodicity index, ergodicity exponent.
Received: 05.10.2023
English version:
Journal of Mathematical Sciences (New York), 2024, Volume 281, Issue 2, Pages 227–233
DOI: https://doi.org/10.1007/s10958-024-07095-z
Document Type: Article
UDC: 512.643
Language: Russian
Citation: Yu. A. Al'pin, V. S. Al'pina, “Ergodicity index of the set of stochastic matrices”, Computational methods and algorithms. Part XXXVI, Zap. Nauchn. Sem. POMI, 524, POMI, St. Petersburg, 2023, 7–17; J. Math. Sci. (N. Y.), 281:2 (2024), 227–233
Citation in format AMSBIB
\Bibitem{AlpAlp23}
\by Yu.~A.~Al'pin, V.~S.~Al'pina
\paper Ergodicity index of the set of stochastic matrices
\inbook Computational methods and algorithms. Part~XXXVI
\serial Zap. Nauchn. Sem. POMI
\yr 2023
\vol 524
\pages 7--17
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7352}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2024
\vol 281
\issue 2
\pages 227--233
\crossref{https://doi.org/10.1007/s10958-024-07095-z}
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