Geodesic
On the Stein–Tikhomirov method and its applications in nonclassical limit theorems
Diskretnaya Matematika, Tome 19 (2007) no. 1, pp. 27-39
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we give necessary and sufficient conditions for validity of the central limit theorem for sums of independent random variables in terms of characteristic functions in a nonclassical setup where an essential contribution of individual variables to the sum is allowed. These conditions are formulated with the use of the Stein–Tikhomirov operator. 
@article{DM_2007_19_1_a4,
     author = {Sh. K. Formanov},
     title = {On the {Stein{\textendash}Tikhomirov} method and its applications in nonclassical limit theorems},
     journal = {Diskretnaya Matematika},
     pages = {27--39},
     year = {2007},
     volume = {19},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2007_19_1_a4/}
}
TY  - JOUR
AU  - Sh. K. Formanov
TI  - On the Stein–Tikhomirov method and its applications in nonclassical limit theorems
JO  - Diskretnaya Matematika
PY  - 2007
SP  - 27
EP  - 39
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DM_2007_19_1_a4/
LA  - ru
ID  - DM_2007_19_1_a4
ER  - 
%0 Journal Article
%A Sh. K. Formanov
%T On the Stein–Tikhomirov method and its applications in nonclassical limit theorems
%J Diskretnaya Matematika
%D 2007
%P 27-39
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/DM_2007_19_1_a4/
%G ru
%F DM_2007_19_1_a4
Sh. K. Formanov. On the Stein–Tikhomirov method and its applications in nonclassical limit theorems. Diskretnaya Matematika, Tome 19 (2007) no. 1, pp. 27-39. http://geodesic.mathdoc.fr/item/DM_2007_19_1_a4/

[1] Stein C., “A bound for the error in the normal approximation to the distribution of a sum of dependent random variables”, Proc. 6th Berkeley Symp. Math. Stat. Probab., v. 2, Univ. California Press, Berkeley, Calif., 1972, 583–602 | MR | Zbl

[2] Stein C., Approximation, computation of expectations, Inst. Math. Statist., Hayward, Calif., 1986 | MR

[3] Tikhomirov A. N., “O skorosti skhodimosti v tsentralnoi predelnoi teoreme dlya slabo zavisimykh velichin”, Teoriya veroyatnostei i ee primeneniya, 25:4 (1980), 800–818 | MR | Zbl

[4] Formanov Sh. K., “Metod Steina–Tikhomirova i neklassicheskaya tsentralnaya predelnaya teorema”, Doklady RAN, 376:4 (2001), 458–460 | MR | Zbl

[5] Petrovskii I. G., Lektsii po teorii obyknovennykh differentsialnykh uravnenii, Nauka, Moskva, 1970

[6] Zolotarev V. M., Sovremennaya teoriya summirovaniya nezavisimykh sluchainykh velichin, Nauka, Moskva, 1986

[7] Rotar V. I., “K obobscheniyu teoremy Lindeberga–Fellera”, Matem. zametki, 18:1 (1975), 129–135 | MR | Zbl

[8] Kiryanova L. V., Rotar V. I., “Otsenka skorosti skhodimosti v tsentralnoi predelnoi teoreme dlya martingalov”, Teoriya veroyatnostei i ee primeneniya, 36 (1991), 301–312 | MR

[9] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, Moskva, 1977