Geodesic
On the transition of distributions of sums of random variables related to the generalised allocation scheme from one lattice to another
Diskretnaya Matematika, Tome 19 (2007) no. 3, pp. 15-21.

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We consider in detail the phenomenon of transition of distributions of sums of independent identically distributed non-negative integer-valued random variables related to the generalised allocation scheme from one lattice to another. 
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A. V. Kolchin; V. F. Kolchin. On the transition of distributions of sums of random variables related to the generalised allocation scheme from one lattice to another. Diskretnaya Matematika, Tome 19 (2007) no. 3, pp. 15-21. http://geodesic.mathdoc.fr/item/DM_2007_19_3_a1/

[1] Kolchin V. F., Sevastyanov B. A., Chistyakov V. P., Sluchainye razmescheniya, Nauka, Moskva, 1984

[2] Kolchin A. V., Kolchin V. F., “O perekhode raspredelenii summ nezavisimykh odinakovo raspredelennykh sluchainykh velichin s odnoi reshetki na druguyu v obobschennoi skheme razmescheniya”, Diskretnaya matematika, 18:4 (2006), 113–127 | MR | Zbl