Geodesic
On the asymptotic normality of some sums of dependent random variables
Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 141-149 Cet article a éte moissonné depuis la source Math-Net.Ru

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A theorem on the asymptotic normality of the sum of dependent random variables is stated and proved. Conditions of the theorem are formulated in terms of a dependency graph which characterizes the relationships between random variables. This theorem is used to prove the asymptotic normality of the sum of functions defined on subsets of elements of the stationary sequence satisfying the strong mixing condition. As an illustration of possible applications of these theorems we give a theorem on the asymptotic normality of the number of empty cells if the random sequence of cells occupied by particles is a stationary sequence satisfying the uniform strong mixing condition.
Keywords: sums of dependent variables, asymptotic normality, dependency graph, strong mixing condition. 
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M. I. Tikhomirova; V. P. Chistyakov. On the asymptotic normality of some sums of dependent random variables. Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 141-149. http://geodesic.mathdoc.fr/item/DM_2015_27_4_a10/

[1] Janson S., “Normal convergence by higher semiinvariants with applications to sums of dependent random variables and random graphs”, Ann. Probab., 16:1 (1988), 305–312 | DOI | MR | Zbl

[2] Mikhailov V.G., “Ob odnoi teoreme Yansona”, Teoriya veroyatn. i ee primen., 36:1 (1991), 168–170 | MR

[3] Leonov V.P., Shiryaev A.N., “K tekhnike vychisleniya semiinvariantov”, Teoriya veroyatn. i ee primen., 4:3 (1959), 342–355 | Zbl

[4] Ibragimov I.A., Linnik Yu.V., Nezavisimye i statsionarno svyazannye velichiny, Nauka, Moskva, 1965, 816 pp.

[5] Rozanov Yu.A., Sluchainye protsessy, Nauka, Moskva, 1979 | MR

[6] Tikhomirova M.I., Chistyakov V.P., “Ob asimptotike momentov chisla nepoyavivshikhsya $s$-tsepochek”, Diskretnaya matematika, 9:1 (1997), 12–29 | DOI | MR | Zbl

[7] Tikhomirova M.I., “Asimptoticheskaya normalnost chisla nepoyavivshikhsya nesploshnykh tsepochek iskhodov nezavisimykh ispytanii”, Diskretnaya matematika, 21:2 (2009), 112–125 | DOI | MR | Zbl

[8] Zubkov A.M., “Tsepi Markova, blizkie k posledovatelnosti nezavisimykh ispytanii”, Matem. zametki, 25:3 (1979), 465–474 | MR