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Teoriya Veroyatnostei i ee Primeneniya, 1996, Volume 41, Issue 1, Pages 89–106
DOI: https://doi.org/10.4213/tvp2777 (Mi tvp2777) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Cubic stochastic matrices and their probability interpretation

V. M. Maksimov

Tver State University
Full-text PDF (1164 kB) Citations (24)
DOI: https://doi.org/10.4213/tvp2777
Abstract: This paper considers associative multiplications of cubic matrices generalizing the ordinary multiplication of matrices. Cubic analogues of stochastic matrices are introduced and their probabilistic interpretations are given. Cubic stationary stochastic matrices are described and the proposition on convergence of a cubic stochastic matrix to a stationary one is proved. We introduce the notion of the Markov interaction process which generalizes the notion of a Markov process and show that the notion of ergodicity of such a process is naturally related with the associative multiplication of cubic matrices.
Keywords: probability, Markov chain, cubic stochastic matrices, Markov interaction process.
Received: 13.06.1995
English version:
Theory of Probability and its Applications, 1997, Volume 41, Issue 1, Pages 55–69
DOI: https://doi.org/10.1137/TPRBAU000041000001000055000001
Bibliographic databases:
Language: Russian
Citation: V. M. Maksimov, “Cubic stochastic matrices and their probability interpretation”, Teor. Veroyatnost. i Primenen., 41:1 (1996), 89–106; Theory Probab. Appl., 41:1 (1997), 55–69
Citation in format AMSBIB
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\by V.~M.~Maksimov
\paper Cubic stochastic matrices and their probability interpretation
\jour Teor. Veroyatnost. i Primenen.
\yr 1996
\vol 41
\issue 1
\pages 89--106
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\zmath{https://zbmath.org/?q=an:0887.15021}
\transl
\jour Theory Probab. Appl.
\yr 1997
\vol 41
\issue 1
\pages 55--69
\crossref{https://doi.org/10.1137/TPRBAU000041000001000055000001}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1997WQ28100004}
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  • https://www.mathnet.ru/eng/tvp2777
  • https://doi.org/10.4213/tvp2777
  • https://www.mathnet.ru/eng/tvp/v41/i1/p89
    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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