Geodesic
The Stein--Tikhomirov Method and a Nonclassical Central Limit Theorem
Matematičeskie zametki, Tome 71 (2002) no. 4, pp. 604-610.

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

We present a simplified version of the Stein–Tikhomirov method realized by defining a certain operator in the class of twice differentiable characteristic functions. Using this method, we establish a criterion for the validity of a nonclassical central limit theorem in terms of characteristic functions. 
@article{MZM_2002_71_4_a11,
     author = {Sh. K. Formanov},
     title = {The {Stein--Tikhomirov} {Method} and a {Nonclassical} {Central} {Limit} {Theorem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {604--610},
     publisher = {mathdoc},
     volume = {71},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_4_a11/}
}
TY  - JOUR
AU  - Sh. K. Formanov
TI  - The Stein--Tikhomirov Method and a Nonclassical Central Limit Theorem
JO  - Matematičeskie zametki
PY  - 2002
SP  - 604
EP  - 610
VL  - 71
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_71_4_a11/
LA  - ru
ID  - MZM_2002_71_4_a11
ER  - 
%0 Journal Article
%A Sh. K. Formanov
%T The Stein--Tikhomirov Method and a Nonclassical Central Limit Theorem
%J Matematičeskie zametki
%D 2002
%P 604-610
%V 71
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2002_71_4_a11/
%G ru
%F MZM_2002_71_4_a11
Sh. K. Formanov. The Stein--Tikhomirov Method and a Nonclassical Central Limit Theorem. Matematičeskie zametki, Tome 71 (2002) no. 4, pp. 604-610. http://geodesic.mathdoc.fr/item/MZM_2002_71_4_a11/

[1] Stein Ch., “A bound for error in the normal approximation to the distribution of a sum of dependent random variables”, Proc. 6th Berkley Symp. Math. Stat. and Prob., V. 2, 1972, 583–602 | Zbl

[2] Tikhomirov A. N., “O skhodimosti ostatochnogo chlena v tsentralnoi predelnoi teoreme dlya slabozavisimykh sluchainykh velichin”, Teoriya veroyatn. i ee primeneniya, 25:4 (1980), 800–818 | MR | Zbl

[3] Linnik Yu. I., Ostrovskii I. V., Razlozheniya sluchainykh velichin i vektorov, Nauka, M., 1972

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

[5] Liptser R. Sh., Shiryaev A. N., Teoriya martingalov, Nauka, M., 1986 | Zbl