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.
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
\Bibitem{Mak96}
\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
\mathnet{http://mi.mathnet.ru/tvp2777}
\crossref{https://doi.org/10.4213/tvp2777}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1404897}
\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}
Linking options:
https://www.mathnet.ru/eng/tvp2777
https://doi.org/10.4213/tvp2777
https://www.mathnet.ru/eng/tvp/v41/i1/p89
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