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
Cet article a éte moissonné depuis 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.
@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/}
}
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/
[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