Geodesic
On the law of large numbers for martingales
Informatics and Automation, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 300-309.

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

Additional constraints are obtained under which sufficient conditions in the classical law of large numbers in a scheme of series for martingales are also necessary. The accuracy of the constraints obtained is demonstrated by examples. 
@article{TRSPY_2014_287_a16,
     author = {P. A. Yaskov},
     title = {On the law of large numbers for martingales},
     journal = {Informatics and Automation},
     pages = {300--309},
     publisher = {mathdoc},
     volume = {287},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_287_a16/}
}
TY  - JOUR
AU  - P. A. Yaskov
TI  - On the law of large numbers for martingales
JO  - Informatics and Automation
PY  - 2014
SP  - 300
EP  - 309
VL  - 287
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2014_287_a16/
LA  - ru
ID  - TRSPY_2014_287_a16
ER  - 
%0 Journal Article
%A P. A. Yaskov
%T On the law of large numbers for martingales
%J Informatics and Automation
%D 2014
%P 300-309
%V 287
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2014_287_a16/
%G ru
%F TRSPY_2014_287_a16
P. A. Yaskov. On the law of large numbers for martingales. Informatics and Automation, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 300-309. http://geodesic.mathdoc.fr/item/TRSPY_2014_287_a16/

[1] de la Peña V.H., Giné E., “Decoupling: From dependence to independence. Randomly stopped processes, $U$-statistics and processes, martingales and beyond”, Springer, New York, 1999 | MR | Zbl

[2] Jacod J., Shiryaev A.N., Limit theorems for stochastic processes, Springer, Berlin, 2003 | MR

[3] Liptser R.Sh., Shiryaev A.N., “O neobkhodimykh i dostatochnykh usloviyakh v funktsionalnoi tsentralnoi predelnoi teoreme dlya semimartingalov”, Teoriya veroyatn. i ee primen., 26:1 (1981), 132–137 | MR | Zbl

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

[5] Yaskov P.A., “Neobkhodimye usloviya v zakone bolshikh chisel dlya martingalov i svyazannykh s nimi sistem”, UMN, 66:4 (2011), 181–182 | DOI | MR | Zbl