An Extension of Central Limit Theorem for Randomly Indexed m-Dependent Random Variables

被引：4

作者：

Belloni, Stefano ^{[1
,2
]}

机构：

[1] Ctr Modeling & Simulat Biosci BIOMS, Heidelberg, Germany

[2] Interdisciplinary Ctr Sci Comp IWR, Heidelberg, Germany

来源：

FILOMAT | 2017年 / 31卷 / 14期

关键词：

Central limit theorem; dependent random variables; stationary sequence;

D O I：

10.2298/FIL1714369B

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we prove a conjecture of Shang about the sum of a random number N-n of independent random variables. The random number N-n is supposed to converge in probability toward a positive random variable.

引用

页码：4369 / 4377

页数：9

共 50 条

[21] Moderate deviation principle for m-dependent random variables*
Yu Miao
Jianan Zhu
Jianyong Mu
Lithuanian Mathematical Journal, 2018, 58 : 54 - 68
[22] On normal approximation for φ-mixing and m-dependent random variables
Sunklodas, Jonas Kazys
LITHUANIAN MATHEMATICAL JOURNAL, 2023, 63 (04) : 524 - 546
[23] On some approximations for sums of m-dependent random variables
Sunklodas, Jonas Kazys
LITHUANIAN MATHEMATICAL JOURNAL, 2023, 63 (02) : 203 - 222
[24] A CENTRAL LIMIT THEOREM FOR STRONG NEAR-EPOCH DEPENDENT RANDOM VARIABLES
LIN ZHENGYAN QIU JIN Department of Mathematics
ChineseAnnalsofMathematics, 2004, (02) : 263 - 274
[25] A central limit theorem for strong near-epoch dependent random variables
Lin, ZY
Qiu, J
CHINESE ANNALS OF MATHEMATICS SERIES B, 2004, 25 (02) : 263 - 274
[26] A note on the almost sure central limit theorem for some dependent random variables
Dudzinski, M
STATISTICS & PROBABILITY LETTERS, 2003, 61 (01) : 31 - 40
[27] On the rates of convergence in weak limit theorems for geometric random sums of the strictly stationary sequence of m-dependent random variables
Tran Loc Hung
Phan TriKien
Lithuanian Mathematical Journal, 2020, 60 : 173 - 188
[28] On the central limit theorem for unsharp quantum random variables
Dimic, Aleksandra
Dakic, Borivoje
NEW JOURNAL OF PHYSICS, 2018, 20
[29] A CENTRAL LIMIT THEOREM FOR TRIANGULAR ARRAYS OF WEAKLY DEPENDENT RANDOM VARIABLES, WITH APPLICATIONS IN STATISTICS
Neumann, Michael H.
ESAIM-PROBABILITY AND STATISTICS, 2013, 17 : 120 - 134
[30] Bounds for the normal approximation of the maximum likelihood estimator from m-dependent random variables
Anastasiou, Andreas
STATISTICS & PROBABILITY LETTERS, 2017, 129 : 171 - 181

← 1 2 3 4 5 →