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

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

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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• http://mi.mathnet.ru/eng/dm1514
• https://doi.org/10.4213/dm1514
• http://mi.mathnet.ru/eng/dm/v30/i3/p141

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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
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