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Diskr. Mat., 2018, Volume 30, Issue 3, Pages 141–158 (Mi dm1514)  

This article is cited in 1 scientific paper (total in 1 paper)

On the distribution of multiple power series regularly varying at the boundary point

A. L. Yakymiv

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Let $B(x)$ be a multiple power series with nonnegative coefficients which is convergent for all $x\in(0,1)^n$ and diverges at the point $\mathbf1=(1,…,1)$. Random vectors (r.v.) $\xi_x$ such that $\xi_x$ has distribution of the power series $B(x)$ type is studied. The integral limit theorem for r.v. $\xi_x$ as $x\uparrow\mathbf1$ is proved under the assumption that $B(x)$ is regularly varying at this point. Also local version of this theorem is obtained under the condition that the coefficients of the series $B(x)$ are one-sided weakly oscillating at infinity.

Keywords: Multiple power series distribution, weak convergence, $\sigma$-finite measures, gamma-distribution, regularly varying functions, one-sided weakly oscillating functions

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations


DOI: https://doi.org/10.4213/dm1514

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English version:
Discrete Mathematics and Applications, 2019, 29:6, 409–421

Bibliographic databases:

UDC: 519.212.2
Received: 03.04.2018

Citation: A. L. Yakymiv, “On the distribution of multiple power series regularly varying at the boundary point”, Diskr. Mat., 30:3 (2018), 141–158; Discrete Math. Appl., 29:6 (2019), 409–421

Citation in format AMSBIB
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\paper On the distribution of multiple power series regularly varying at the boundary point
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\pages 141--158
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\jour Discrete Math. Appl.
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\vol 29
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\pages 409--421
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  • https://doi.org/10.4213/dm1514
  • http://mi.mathnet.ru/eng/dm/v30/i3/p141

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. L. Yakymiv, “Abelian theorem for the regularly varying measure and its density in orthant”, Theory Probab. Appl., 64:3 (2019), 385–400  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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