Geodesic
On the rate of convergence in the strong law of large numbers for non-negative random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 183-194 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We study the rate of convergence in the strong law of large numbers for sequences of non-negative random variables without the independence assumption. We obtain conditions for which an analog of the Baum–Katz theorem holds. 
@article{ZNSL_2016_454_a10,
     author = {V. M. Korchevsky},
     title = {On the rate of convergence in the strong law of large numbers for non-negative random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {183--194},
     year = {2016},
     volume = {454},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a10/}
}
TY  - JOUR
AU  - V. M. Korchevsky
TI  - On the rate of convergence in the strong law of large numbers for non-negative random variables
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 183
EP  - 194
VL  - 454
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a10/
LA  - ru
ID  - ZNSL_2016_454_a10
ER  - 
%0 Journal Article
%A V. M. Korchevsky
%T On the rate of convergence in the strong law of large numbers for non-negative random variables
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 183-194
%V 454
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a10/
%G ru
%F ZNSL_2016_454_a10
V. M. Korchevsky. On the rate of convergence in the strong law of large numbers for non-negative random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 183-194. http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a10/

[1] V. M. Korchevskii, V. V. Petrov, “Ob usilennom zakone bolshikh chisel dlya posledovatelnostei zavisimykh sluchainykh velichin”, Vestnik SPbGU. Ser. 1, 2010, no. 3, 26–30

[2] V. V. Petrov, “Ob usilennom zakone bolshikh chisel”, Teoriya veroyatn. i ee primen., 14:2 (1969), 193–202 | MR | Zbl

[3] V. V. Petrov, Summy nezavisimykh sluchainykh velichin, Nauka, M., 1972 | MR

[4] V. V. Petrov, Predelnye teoremy dlya summ nezavisimykh sluchainykh velichin, Nauka, M., 1987 | MR

[5] V. V. Petrov, “Ob usilennom zakone bolshikh chisel dlya posledovatelnosti neotritsatelnykh sluchainykh velichin”, Teoriya veroyatn. i ee primen., 53:2 (2008), 379–382 | DOI | Zbl

[6] V. V. Petrov, “Ob ustoichivosti summ neotritsatelnykh sluchainykh velichin”, Zap. nauchn. semin. POMI, 361, 2008, 78–82 | Zbl

[7] P. Chen, S. H. Sung, “A strong law of large numbers for nonnegative random variables and applications”, Statist. Probab. Letters, 118 (2016), 80–86 | DOI | MR | Zbl

[8] V. Korchevsky, “A generalization of the Petrov strong law of large numbers”, Statist. Probab. Letters, 104 (2015), 102–108 | DOI | MR | Zbl

[9] A. Kuczmaszewska, “Convergence rate in the Petrov SLLN for dependent random variables”, Acta Math. Hungar., 148 (2016), 56–72 | DOI | MR

[10] G. Stoica, “Rate of convergence in Petrov's strong law of large numbers”, Adv. Appl. Statist. Sci., 4 (2010), 57–60 | MR | Zbl