Geodesic
On absolute convergence of series of random variables almost surely
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 140-144 
V. V. Petrov. On absolute convergence of series of random variables almost surely. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 140-144. http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a8/
@article{ZNSL_2014_431_a8,
     author = {V. V. Petrov},
     title = {On absolute convergence of series of random variables almost surely},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {140--144},
     year = {2014},
     volume = {431},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a8/}
}
TY  - JOUR
AU  - V. V. Petrov
TI  - On absolute convergence of series of random variables almost surely
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 140
EP  - 144
VL  - 431
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a8/
LA  - ru
ID  - ZNSL_2014_431_a8
ER  - 
%0 Journal Article
%A V. V. Petrov
%T On absolute convergence of series of random variables almost surely
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 140-144
%V 431
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a8/
%G ru
%F ZNSL_2014_431_a8

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper deals with the conditions of absolute convergence of series of random variables almost surely. The results contain no independence assumptions. A generalization is obtained in analytical terms.

[1] E. R. van Kampen, “Infinite product measures and infinite convolutions”, Amer. J. Math., 62 (1940), 417–448 | DOI | MR | Zbl

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

[3] V. V. Petrov, “O poryadke rosta summ zavisimykh sluchainykh velichin”, Teoriya veroyatn. i eë primen., 18:2 (1973), 358–361 | MR | Zbl

[4] V. V. Petrov, “O roste summ izmerimykh funktsii”, Litovskii matem. sb., 16:1 (1976), 189–192 | Zbl

[5] V. V. Petrov, Limit Theorems of Probability Theory, Oxford University Press, New York, 1995 | MR | Zbl