Geodesic
On the law of large numbers for martingales
Informatics and Automation, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 300-309 
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/
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_287_a16/}
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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.

[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