Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 132, Pages 105–108 (Mi into176)  
On the stability of a linear system of difference equations with random parameters

L. I. Rodina

Udmurt State University, Mathematical Department
Full-text PDF (272 kB)
Abstract: We study the asymptotic behavior of solutions to a linear system of difference equation whose right-hand side at each time moment depends not only on the value at the previous moment, but also on a random parameter that takes its values in a given set. We obtain conditions of the Lyapunov stability and the asymptotic stability of the equilibrium position that are valid for all values of the random parameter or with probability 1.
Keywords: system of difference equations with random parameters, Lyapunov stability, asymptotic stability, stability with probability 1.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00346_à
Ministry of Education and Science of the Russian Federation 2003
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 230, Issue 5, Pages 757–761
DOI: https://doi.org/10.1007/s10958-018-3784-2
Bibliographic databases:
Document Type: Article
UDC: 517.962.22
MSC: 37A50, 37H10
Language: Russian
Citation: L. I. Rodina, “On the stability of a linear system of difference equations with random parameters”, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 132, VINITI, Moscow, 2017, 105–108; J. Math. Sci. (N. Y.), 230:5 (2018), 757–761
Citation in format AMSBIB
\Bibitem{Rod17}
\by L.~I.~Rodina
\paper On the stability of a linear system of difference equations with random parameters
\inbook Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 132
\pages 105--108
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into176}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801396}
\zmath{https://zbmath.org/?q=an:1391.39024}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 230
\issue 5
\pages 757--761
\crossref{https://doi.org/10.1007/s10958-018-3784-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044455475}
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