Geodesic
On stability of sums of nonnegative random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 78-82 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present sufficient conditions for stability of sums of nonnegative random variables having finite moments of the second order. We demonstrate that these conditions are nonimprovable in some sense. Bibl. – 4 titles. 
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V. V. Petrov. On stability of sums of nonnegative random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 78-82. http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a5/

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[2] N. Etemadi, “Stability of sums of weighted nonnegative random variables”, J. Multivariate Analysis, 13 (1983), 361–365 | DOI | MR | Zbl

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

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