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Criteria of relative and stochastic compactness for distributions of sums of independent random variables. / Khartov, A. A.

In: Theory of Probability and its Applications, Vol. 63, No. 1, 01.01.2018, p. 57-71.

Research output: Contribution to journal › Article › peer-review

Harvard

Khartov, AA 2018, 'Criteria of relative and stochastic compactness for distributions of sums of independent random variables', Theory of Probability and its Applications, vol. 63, no. 1, pp. 57-71. https://doi.org/10.1137/S0040585X97T988915

APA

Khartov, A. A. (2018). Criteria of relative and stochastic compactness for distributions of sums of independent random variables. Theory of Probability and its Applications, 63(1), 57-71. https://doi.org/10.1137/S0040585X97T988915

Vancouver

Khartov AA. Criteria of relative and stochastic compactness for distributions of sums of independent random variables. Theory of Probability and its Applications. 2018 Jan 1;63(1):57-71. https://doi.org/10.1137/S0040585X97T988915

Author

Khartov, A. A. / Criteria of relative and stochastic compactness for distributions of sums of independent random variables. In: Theory of Probability and its Applications. 2018 ; Vol. 63, No. 1. pp. 57-71.

BibTeX

@article{78a983b634a746fe9eff3bacae1b6527,
title = "Criteria of relative and stochastic compactness for distributions of sums of independent random variables",
abstract = "We consider sequences of distributions of centered sums of independent random variables within the scheme of series without imposing the classical conditions of uniform asymptotic negligibility and uniform asymptotic constancy. A criterion of relative compactness for such sequences of distributions was obtained by Siegel [Lith. Math. J., 21 (1981), pp. 331–341]. In the present paper this criterion is formulated in a more complete form, and a new proof is proposed based on characteristic functions. We also obtain a criterion of stochastic compactness, which is a stronger property than the one introduced by Feller [Proc. 5th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, 1965/66, Vol. 2: Contributions to Probability Theory, Part 1, 1967, pp. 373–388]. Moreover, several new criteria of relative and stochastic compactness for such sequences of distributions are proposed in terms of characteristic functions of summable random variables.",
keywords = "Characteristic functions, Relative compactness, Scheme of series, Stochastic compactness, Sums of independent random variables",
author = "Khartov, {A. A.}",
year = "2018",
month = jan,
day = "1",
doi = "10.1137/S0040585X97T988915",
language = "English",
volume = "63",
pages = "57--71",
journal = "Theory of Probability and its Applications",
issn = "0040-585X",
publisher = "Society for Industrial and Applied Mathematics",
number = "1",

}

RIS

TY - JOUR

T1 - Criteria of relative and stochastic compactness for distributions of sums of independent random variables

AU - Khartov, A. A.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We consider sequences of distributions of centered sums of independent random variables within the scheme of series without imposing the classical conditions of uniform asymptotic negligibility and uniform asymptotic constancy. A criterion of relative compactness for such sequences of distributions was obtained by Siegel [Lith. Math. J., 21 (1981), pp. 331–341]. In the present paper this criterion is formulated in a more complete form, and a new proof is proposed based on characteristic functions. We also obtain a criterion of stochastic compactness, which is a stronger property than the one introduced by Feller [Proc. 5th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, 1965/66, Vol. 2: Contributions to Probability Theory, Part 1, 1967, pp. 373–388]. Moreover, several new criteria of relative and stochastic compactness for such sequences of distributions are proposed in terms of characteristic functions of summable random variables.

AB - We consider sequences of distributions of centered sums of independent random variables within the scheme of series without imposing the classical conditions of uniform asymptotic negligibility and uniform asymptotic constancy. A criterion of relative compactness for such sequences of distributions was obtained by Siegel [Lith. Math. J., 21 (1981), pp. 331–341]. In the present paper this criterion is formulated in a more complete form, and a new proof is proposed based on characteristic functions. We also obtain a criterion of stochastic compactness, which is a stronger property than the one introduced by Feller [Proc. 5th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, 1965/66, Vol. 2: Contributions to Probability Theory, Part 1, 1967, pp. 373–388]. Moreover, several new criteria of relative and stochastic compactness for such sequences of distributions are proposed in terms of characteristic functions of summable random variables.

KW - Characteristic functions

KW - Relative compactness

KW - Scheme of series

KW - Stochastic compactness

KW - Sums of independent random variables

UR - http://www.scopus.com/inward/record.url?scp=85064689639&partnerID=8YFLogxK

U2 - 10.1137/S0040585X97T988915

DO - 10.1137/S0040585X97T988915

M3 - Article

AN - SCOPUS:85064689639

VL - 63

SP - 57

EP - 71

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 1

ER -

ID: 52420542