Rate of convergence to the uniform distribution for autoregression scheme on the finite Abelian group
Matematičeskie voprosy kriptografii, Tome 9 (2018) no. 1, pp. 65-74 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The linear autoregression scheme with random control on finite Abelian group is considered. Inequalities for the mean-square deviation of distributions of its elements from the uniform distribution are obtained.
@article{MVK_2018_9_1_a3,
     author = {I. A. Kruglov},
     title = {Rate of convergence to the uniform distribution for autoregression scheme on the finite {Abelian} group},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {65--74},
     year = {2018},
     volume = {9},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2018_9_1_a3/}
}
TY  - JOUR
AU  - I. A. Kruglov
TI  - Rate of convergence to the uniform distribution for autoregression scheme on the finite Abelian group
JO  - Matematičeskie voprosy kriptografii
PY  - 2018
SP  - 65
EP  - 74
VL  - 9
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MVK_2018_9_1_a3/
LA  - ru
ID  - MVK_2018_9_1_a3
ER  - 
%0 Journal Article
%A I. A. Kruglov
%T Rate of convergence to the uniform distribution for autoregression scheme on the finite Abelian group
%J Matematičeskie voprosy kriptografii
%D 2018
%P 65-74
%V 9
%N 1
%U http://geodesic.mathdoc.fr/item/MVK_2018_9_1_a3/
%G ru
%F MVK_2018_9_1_a3
I. A. Kruglov. Rate of convergence to the uniform distribution for autoregression scheme on the finite Abelian group. Matematičeskie voprosy kriptografii, Tome 9 (2018) no. 1, pp. 65-74. http://geodesic.mathdoc.fr/item/MVK_2018_9_1_a3/

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

[2] Kruglov I. A., “Sluchainye posledovatelnosti vida $X_{t+1}=a_t\cdot X_t+b_t\pmod n$ s zavisimymi koeffitsientami $a_t, b_t$”, Diskretnaya matematika, 17:2 (2005), 49–55 | DOI | Zbl

[3] Hildebrand M., “Random processes of the form $X_{n+1} = a_n\cdot X_n+b_n\pmod p$”, Ann. Probab., 21 (1993), 710–720 | DOI | MR | Zbl

[4] Hildebrand M., “Random processes of the form $X_{n+1} = a_n\cdot X_n+b_n\pmod p$, where $b_n$ takes on a single value”, Random Discrete Structures, IMA Vol. Math. Appl., 76, 1996, 153–174 | MR | Zbl

[5] Bianko S., Random processes of the form $X_{n+1}=A_n\cdot X_n+B_n\pmod p$ in two dimensions, Ph.D., State Univ. of New York at Albany, 2012, 37 pp. | MR

[6] Kruglov I. A., “Skhodimost matrits perekhodnykh veroyatnostei nekotorykh tsepei Markova na konechnoi abelevoi gruppe k ravnomernoi matritse”, Matematicheskie voprosy kriptografii, 8:1 (2017), 31–50 | DOI

[7] Gantmakher F. R., Teoriya matrits, Nauka, M., 1966, 576 pp. | MR