Geodesic
On the stability of a linear system of difference equations with random parameters
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 105-108.

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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. 
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     author = {L. I. Rodina},
     title = {On the stability of a linear system of difference equations with random parameters},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {105--108},
     publisher = {mathdoc},
     volume = {132},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_132_a23/}
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L. I. Rodina. On the stability of a linear system of difference equations with random parameters. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 105-108. http://geodesic.mathdoc.fr/item/INTO_2017_132_a23/