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

[1] A central limit theorem for randomly indexed m-dependent random variables
Shang, Yilun
[J]. FILOMAT, 2012, 26 (04) : 713 - 717
[2] ON THE CENTRAL LIMIT THEOREM FOR M-DEPENDENT VARIABLES
DIANANDA, PH
[J]. ANNALS OF MATHEMATICAL STATISTICS, 1954, 25 (02): : 412 - 413
[3] ON THE ORDER OF APPROXIMATION IN THE RANDOM CENTRAL LIMIT THEOREM FOR m-DEPENDENT RANDOM VARIABLES
Rao, B. L. S. Prakasa
Sreehari, M.
[J]. PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, 2016, 36 (01): : 47 - 57
[4] Quantitative bounds in the central limit theorem for m-dependent random variables
Janson, Svante
Pratelli, Luca
Rigo, Pietro
[J]. ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2024, 21 : 245 - 265
[5] A central limit theorem for m-dependent random variables under sublinear expectations
Xin-peng Li
[J]. Acta Mathematicae Applicatae Sinica, English Series, 2015, 31 : 435 - 444
[6] A Central Limit Theorem for m-dependent Random Variables under Sublinear Expectations
Li, Xin-peng
[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2015, 31 (02): : 435 - 444
[7] A Central Limit Theorem for m-dependent Random Variables under Sublinear Expectations
Xin-peng LI
[J]. Acta Mathematicae Applicatae Sinica, 2015, 31 (02) : 435 - 444
[8] A more general central limit theorem for m-dependent random variables with unbounded m
Romano, JP
Wolf, M
[J]. STATISTICS & PROBABILITY LETTERS, 2000, 47 (02) : 115 - 124
[9] Central limit theorem for dependent multidimensionally indexed random variables
Christofides, TC
Mavrikiou, PM
[J]. STATISTICS & PROBABILITY LETTERS, 2003, 63 (01) : 67 - 78
[10] ON THE CONVERGENCE RATE IN THE CENTRAL LIMIT-THEOREM FOR M-DEPENDENT RANDOM-VARIABLES
SHERGIN, VV
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 1979, 24 (04) : 782 - 796

← 1 2 3 4 5 →