This article is cited in 2 papers

On limit distribution of sums of random variables

Sergey V. Chebotarev

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

Abstract: Centered Rademacher sequences and centered sequences of lattice random variables with a non-trivial weak limit of the sums $ \frac{1}{\sqrt{n}}\sum\limits_{i=1}^n\xi_i$ are considered in the article. A general form of limit distribution is found for these sequences. It is shown that the form of limit distribution depends only on the average mixed moments of the first order characterizing random variables of the sequence. In the case of lattice random variables we mean a sequence of Rademacher random variables in which we can distribute the elements of the given sequence.

Keywords: sequences of random variables, sum of random variables, sum of dependent random variables, limit distribution.

UDC: 519.21

Received: 24.06.2015
Received in revised form: 29.12.2015
Accepted: 12.01.2016

Language: English

DOI: 10.17516/1997-1397-2016-9-1-17-29

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