Geodesic
Asymptotic normality in a scheme of finitely dependent distribution of particles in cells
Sbornik. Mathematics, Tome 47 (1984) no. 2, pp. 499-512 
V. G. Mikhailov. Asymptotic normality in a scheme of finitely dependent distribution of particles in cells. Sbornik. Mathematics, Tome 47 (1984) no. 2, pp. 499-512. http://geodesic.mathdoc.fr/item/SM_1984_47_2_a12/
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     title = {Asymptotic normality in a scheme of finitely dependent distribution of particles in cells},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A scheme of finitely dependent (and, generally speaking, nonstationary) distribution of particles in a countable collection of cells is considered. Sufficient conditions are given for asymptotic normality of the random variables $\mu_r$ (the number of cells containing exactly $r$ particles each), $\mu$ (the number of occupied cells), and $\xi_r$ (the number of $r$-fold repetitions). For $\mu_r$ these conditions correspond to the “left intermediate domain of variation of the parameters”, while for $\xi_r$ they include also the “central domain”. The method of moments is used in the proof. Bibliography: 6 titles.

[1] Kolchin V. F., Sevastyanov B. A., Chistyakov V. P., Sluchainye razmescheniya, Nauka, M., 1976 | MR | Zbl

[2] Zubkov A. M., Mikhailov V. G., “O povtoreniyakh $s$-tsepochek v posledovatelnosti nezavisimykh ispytanii”, Teoriya veroyatnostei, XXIV:2 (1979), 267–279 | MR

[3] Mikhailov V. G., “Tsentralnaya predelnaya teorema dlya skhemy nezavisimogo razmescheniya chastits po yacheikam”, Trudy Matem. in-ta im. V. A. Steklova AN SSSR, 157 (1981), 138–152 | MR

[4] Zubkov A. M., “Neravenstva dlya veroyatnostei perekhodov s zaprescheniyami i ikh primeneniya”, Matem .sb., 109 (151) (1979), 491–532 | MR | Zbl

[5] Mikhailov V. G., “Otsenka skorosti skhodimosti k raspredeleniyu Puassona pri razmeschenii chastits komplektami”, Teoriya veroyatnostei, XXII:3 (1977), 566–574

[6] Sevastyanov B. A., “Predelnye teoremy v odnoi skheme razmescheniya chastits po yacheikam”, Teoriya veroyatnostei, XI:4 (1966), 696–700