This article is cited in 1 paper

On the limit distribution of sums of real random variables

Sergey V. Chebotarev

Altai state pedagogical university, Molodezhnaya, 55, Barnaul, 656015, Russia

Abstract: Considers centered sequence of absolutely continuous random variables with a non-trivial weak limit of the sums $\displaystyle \frac{1}{\sqrt{n}}\sum \limits_{i=1}^n\xi_i$. We found a general view of the limit distribution. It is shown that the form of the limit distribution depends only on the average mixed moments of the first order, describing the sequence of Rademacher random variables, into which can be decomposed the elements of the given sequence.

Keywords: dependent random variables, the sums of dependent random variables, limit distribution of sums of random variables, the normality of the limit distribution of sums of random variables.

UDC: 519.21

Received: 28.10.2016
Received in revised form: 12.12.2016
Accepted: 10.03.2017

Language: English

DOI: 10.17516/1997-1397-2017-10-3-310-313

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