Hilbert空间中加权相关随机向量的广义Marcinkiewicz定律

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Theory of Probability and its Applications Pub Date : 2022-11-07 DOI:10.1137/s0040585x97t991039

T. C. Son, L. V. Dung, D. T. Dat, T. T. Trang

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引用次数: 0

摘要

概率论及其应用，67卷，第3期，第434-451页，2022年11月。本文的目的是应用正则变函数理论研究加权和$S_n=\sum_{j=1}^{m_n}c_{nj}X_j$的Marcinkiewicz弱和强定律，其中$(X_n;\, n\geq 1)$是Hilbert空间中的一个相关随机向量序列，$(c_{nj})$是一个实数数组。应用这些结果，得到了多元Pareto—Zipf分布和多元log-gamma分布收敛性的一些结果。

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Generalized Marcinkiewicz Laws for Weighted Dependent Random Vectors in Hilbert Spaces

Theory of Probability &Its Applications, Volume 67, Issue 3, Page 434-451, November 2022.
The aim of this paper is to apply the theory of regularly varying functions for studying Marcinkiewicz weak and strong laws of large numbers for the weighted sum $S_n=\sum_{j=1}^{m_n}c_{nj}X_j$, where $(X_n;\, n\geq 1)$ is a sequence of dependent random vectors in Hilbert spaces, and $(c_{nj})$ is an array of real numbers. Moreover, these results are applied to obtain some results on the convergence of multivariate Pareto--Zipf distributions and multivariate log-gamma distributions.

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来源期刊

Theory of Probability and its Applications 数学-统计学与概率论

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

6 months

期刊介绍： Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.