Email this article Characteristic Functions and Compactness of Distributions of Sums of Independent Random Variables
- Authors: Khartov A.A.1,2
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Affiliations:
- St.Petersburg State University
- St.Petersburg National Research University of Information Technologies, Mechanics and Optics
- Issue: Vol 229, No 6 (2018)
- Pages: 792-802
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/240582
- DOI: https://doi.org/10.1007/s10958-018-3719-y
- ID: 240582
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Abstract
The sequences of distributions of centered sums of independent random variables are considered within the framework of the series scheme, without assuming the classical conditions for uniform asymptotic smallness and uniform limit constancy. Necessary and sufficient conditions are obtained for relative and stochastic compactness of such sequences in terms of the characteristic functions of summable random variables and with using their τ-centers.
About the authors
A. A. Khartov
St.Petersburg State University; St.Petersburg National Research University of Information Technologies, Mechanics and Optics
Author for correspondence.
Email: alexeykhartov@gmail.com
Russian Federation, St.-Petersburg
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