Geodesic
Multi-dimensional limit theorem on large deviations for endomorphisms of Euclidean space
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 2, pp. 16-24 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We prove a central limit theorem on large deviations for a sequence with elements being formed by the values of a continuous vector function periodic in each variable, which represents the trajectories of the endomorphisms of the $d$-dimensional Euclidean space in the $m$-dimensional Euclidean space.
Keywords: limit theorem, endomorphisms, large deviations. 
@article{UZKU_2014_156_2_a1,
     author = {F. G. Gabbasov and V. T. Dubrovin},
     title = {Multi-dimensional limit theorem on large deviations for endomorphisms of {Euclidean} space},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {16--24},
     year = {2014},
     volume = {156},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2014_156_2_a1/}
}
TY  - JOUR
AU  - F. G. Gabbasov
AU  - V. T. Dubrovin
TI  - Multi-dimensional limit theorem on large deviations for endomorphisms of Euclidean space
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2014
SP  - 16
EP  - 24
VL  - 156
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UZKU_2014_156_2_a1/
LA  - ru
ID  - UZKU_2014_156_2_a1
ER  - 
%0 Journal Article
%A F. G. Gabbasov
%A V. T. Dubrovin
%T Multi-dimensional limit theorem on large deviations for endomorphisms of Euclidean space
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2014
%P 16-24
%V 156
%N 2
%U http://geodesic.mathdoc.fr/item/UZKU_2014_156_2_a1/
%G ru
%F UZKU_2014_156_2_a1
F. G. Gabbasov; V. T. Dubrovin. Multi-dimensional limit theorem on large deviations for endomorphisms of Euclidean space. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 2, pp. 16-24. http://geodesic.mathdoc.fr/item/UZKU_2014_156_2_a1/

[1] Leonov V. P., Nekotorye prilozheniya starshikh semiinvariantov v teorii sluchainykh protsessov, Nauka, M., 1964, 69 pp. | MR | Zbl

[2] Gabbasov F. G., Dubrovin V. T., “Otsenka skorosti skhodimosti v mnogomernoi predelnoi teoreme dlya endomorfizmov evklidova prostranstva”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 155, no. 2, 2013, 33–43

[3] Dubrovin V. T., “Bolshie ukloneniya v tsentralnoi predelnoi teoreme dlya endomorfizmov evklidova prostranstva”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 153, no. 1, 2011, 195–210

[4] von Bahr B., “Multi-dimensional integral limit theorems for large deviations”, Ark. Mat., 7:1 (1967), 89–99 | DOI | MR | Zbl

[5] Dubrovin V. T., Moskvin D. A., “O raspredelenii drobnykh dolei odnogo klassa preobrazovanii evklidovykh prostranstv”, Veroyatnostnye metody i kibernetika, 9, Kazan. gos. un-t, Kazan, 1971, 45–46 | MR

[6] Sadikova S. M., “Rasstoyaniya mezhdu raspredeleniyami, svyazannye s ikh znacheniyami na vypuklykh mnozhestvakh”, Dokl. AN SSSR, 176:4 (1967), 787–789 | MR | Zbl

[7] Sadikova S. M., “O mnogomernoi tsentralnoi predelnoi teoreme”, Teoriya veroyatnosti i eë primeneniya (Kazan), 13:1 (1968), 164–170 | MR | Zbl