This article is cited in 2 papers

On the asymptotic normality of some sums of dependent random variables

M. I. Tikhomirova^a, V. P. Chistyakov<sup>b

a</sup> Academy of Cryptography of Russian Federation
^b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: 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.

UDC: 519.214.5

Received: 12.01.2015

DOI: 10.4213/dm1353

 English version: Discrete Mathematics and Applications, 2017, 27:2, 123–129

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