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

Regularly Varying Multiple Power Series and it's Distributions

A. L. Yakymiv

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: A multiple power series $B(x)$ with non-negative coefficients converging in $x\in(0,1)^n$ and diverging at the point $\mathbf1=(1,…,1)$ is considered. A random variable (r.v.) $\xi_x$ having power series distribution $B(x)$ is studied. The integral limit theorem for r.v. $\xi_x$ as $x\uparrow\mathbf1$ is proved under the assumption that $B(x)$ regularly varies at this point. Also local version of this theorem is received in the situation when the coefficients of the series $B(x)$ are one-sided weakly oscillatory at infinity.

Keywords: Multiple power series distribution, weak convergence of $\sigma$-finite measures and random vectors, gamma-distribution with parameter $\lambda\geq0$, regularly varying and one-sided weakly oscillatory functions in a positive hyper-octant.

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


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

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Document Type: Article
UDC: 519.212.2
Received: 03.04.2018

Citation: A. L. Yakymiv, “Regularly Varying Multiple Power Series and it's Distributions”, Diskr. Mat., 30:3 (2018), 141–158

Citation in format AMSBIB
\Bibitem{Yak18}
\by A.~L.~Yakymiv
\paper Regularly Varying Multiple Power Series and it's Distributions
\jour Diskr. Mat.
\yr 2018
\vol 30
\issue 3
\pages 141--158
\mathnet{http://mi.mathnet.ru/dm1514}
\crossref{https://doi.org/10.4213/dm1514}
\elib{http://elibrary.ru/item.asp?id=35410176}


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