Geodesic
Autoregression on a~finite Abelian group controlled by a~Markov chain
Matematičeskie voprosy kriptografii, Tome 2 (2011), pp. 25-36.

Voir la notice de l'article provenant de la source Math-Net.Ru

An analog of convergence principle due to B. M. Kloss is proved for autoregressive sequences of random variables on a finite Abelian group controlled by a Markov chain. 
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I. A. Kruglov. Autoregression on a~finite Abelian group controlled by a~Markov chain. Matematičeskie voprosy kriptografii, Tome 2 (2011), pp. 25-36. http://geodesic.mathdoc.fr/item/MVK_2011_2_a1/

[1] Bakhturin Yu. A., Osnovnye struktury sovremennoi algebry, Nauka, Gl. red. fiz.-mat. lit., M., 1990, 320 pp. | MR | Zbl

[2] Gorchinskii Yu. N., Kruglov I. A., Kapitonov V. M., “Voprosy teorii raspredelenii na konechnykh gruppakh”, Trudy po diskretnoi matematike, 1, TVP, M., 1997, 85–112 | MR | Zbl

[3] Egorov B. A., Maksimov Yu. I., “Ob odnoi posledovatelnosti sluchainykh velichin, prinimayuschikh znacheniya iz kompaktnoi kommutativnoi gruppy”, Teoriya veroyatn. i ee primen., 13:4 (1968), 621–630 | MR | Zbl

[4] Kruglov I. A., “Usloviya predelnoi ravnoveroyatnosti sostoyanii registrov sdviga”, Matematicheskie voprosy kriptografii, 1:2 (2010), 19–29

[5] Kloss B. M., “O veroyatnostnykh raspredeleniyakh na bikompaktnykh topologicheskikh gruppakh”, Teoriya veroyatn. i ee primen., 4:3 (1959), 255–290 | MR

[6] Romanovskii V. I., Diskretnye tsepi Markova, Gostekhizdat, M., 1949