RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Diskr. Mat.: Year: Volume: Issue: Page: Find

 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

Full text: PDF file (536 kB)
First page: PDF file
References: PDF file   HTML file

Document Type: Article
UDC: 519.212.2

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}