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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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},
     year = {2022},
     volume = {515},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_515_a13/}
}
TY  - JOUR
AU  - K. A. Tregubova
AU  - A. A. Khartov
TI  - Sums of independent random variables and the generalized Dickman laws
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2022
SP  - 199
EP  - 213
VL  - 515
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2022_515_a13/
LA  - ru
ID  - ZNSL_2022_515_a13
ER  - 
%0 Journal Article
%A K. A. Tregubova
%A A. A. Khartov
%T Sums of independent random variables and the generalized Dickman laws
%J Zapiski Nauchnykh Seminarov POMI
%D 2022
%P 199-213
%V 515
%U http://geodesic.mathdoc.fr/item/ZNSL_2022_515_a13/
%G ru
%F ZNSL_2022_515_a13
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/

[1] B. V. Gnedenko, A. N. Kolmogorov, Predelnye raspredeleniya dlya summ nezavisimykh sluchainykh velichin, Gostekhizdat, M.–L., 1949 | MR

[2] E. Lukach, Kharakteristicheskie funktsii, Nauka, M., 1979

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

[4] A. A. Khartov, “Kriterii otnositelnoi i stokhasticheskoi kompaktnosti raspredelenii summ nezavisimykh sluchainykh velichin”, Teor. veroyatn. prilozh., 63:1 (2018), 70–88 | MR

[5] A. N. Shiryaev, Veroyatnost - 1, MTsNMO, M., 2004

[6] R. Arratia, A. Barbour, S. Tavaré, Logarithmic Combinatorial Structures: A Probabilistic Approach, EMS Monographs in Mathematics, EMS, Zurich, 2003 | DOI | MR

[7] C. Bhattacharjee, L. Goldstein, “Dickman approximation in simulation, summations and perpetuities”, Bernoulli, 25:4A (2019), 2758–2792 | MR

[8] K. Dickman, “On the frequency of numbers containing prime factors of a certain relative magnitude”, Ark. for Mat., 22 (1930), 1–14

[9] D. Hensley, “The convolution powers of the Dickman function”, J. London Math. Soc., 33:2 (1986), 395–406 | DOI | MR

[10] S. A. Molchanov, V. A. Panov, “The Dickman–Goncharov distribution”, Russ. Math. Surv., 75:6 (2020), 1089–1132 | DOI | MR

[11] M. D. Penrose, A. R. Wade, “Random minimal directed spanning trees and Dickman-type distributions”, Adv. Appl. Probab., 36:3 (2004), 691–714 | DOI | MR

[12] R. G. Pinsky, “On the strange domain of attraction to generalized Dickman distributions for sums of independent random variables”, Electron. J. Probab., 23:3 (2018), 1–17 | MR

[13] G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, Graduate Studies Math., 163, AMS, Providence, Rhode Island, 2015 | DOI | MR