Geodesic
Sums of independent random variables and the generalized Dickman laws
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 33, Tome 515 (2022), pp. 199-213

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The probabilistic Dickman law, defined by the known Dickman function, and its generalized versions are considered. In the paper, we obtain a general criterion of the weak convergence to these laws for the distributions of sums of independent non-negative random variables within the series scheme in the classical setting. Moreover, we get a special criterion of the convergence for the case when the summing random variables have finite expectations. 
@article{ZNSL_2022_515_a13,
     author = {K. A. Tregubova and A. A. Khartov},
     title = {Sums of independent random variables and the generalized {Dickman} laws},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {199--213},
     publisher = {mathdoc},
     volume = {515},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_515_a13/}
}
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K. A. Tregubova; A. A. Khartov. Sums of independent random variables and the generalized Dickman laws. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 33, Tome 515 (2022), pp. 199-213. http://geodesic.mathdoc.fr/item/ZNSL_2022_515_a13/