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

[31] LIMIT DISTRIBUTIONS OF SUMS OF M-DEPENDENT BERNOULLI RANDOM-VARIABLES
HUDSON, WN
TUCKER, HG
VEEH, JA
PROBABILITY THEORY AND RELATED FIELDS, 1989, 82 (01) : 9 - 17
[32] ON CENTRAL LIMIT THEOREM FOR SUMS OF DEPENDENT RANDOM VARIABLES
ROSEN, B
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1967, 7 (01): : 48 - &
[33] A NONUNIFORM ESTIMATE OF THE RATE OF CONVERGENCE IN THE CENTRAL LIMIT-THEOREM FOR M-DEPENDENT RANDOM-FIELDS
RAO, BLSP
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1981, 58 (02): : 247 - 256
[34] General Central Limit Theorems for m-Dependent Random Variables Under Sub-linear Expectations
Gu, Wang-Yun
Zhang, Li-Xin
COMMUNICATIONS IN MATHEMATICS AND STATISTICS, 2024,
[35] On the strong limit theorems for double arrays of blockwise M-dependent random variables
Ulrich Stadtmüller
Le Van Thanh
Acta Mathematica Sinica, English Series, 2011, 27 : 1923 - 1934
[36] On the almost sure central limit theorem for randomly indexed sums
Krajka, A.
Wasiura, J.
MATHEMATISCHE NACHRICHTEN, 2009, 282 (04) : 569 - 580
[37] On the Strong Limit Theorems for Double Arrays of Blockwise M-dependent Random Variables
Stadtmueller, Ulrich
Le Van Thanh
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2011, 27 (10) : 1923 - 1934
[38] Central limit theorem for certain classes of dependent random variables
Kaminski, M.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2007, 51 (02) : 335 - 342
[39] Central limit theorem for sampled sums of dependent random variables
Guillotin-Plantard, Nadine
Prieur, Clémentine
ESAIM - Probability and Statistics, 2010, 14 (06) : 299 - 314
[40] A CENTRAL LIMIT THEOREM FOR META-DEPENDENT RANDOM VARIABLES
OREY, S
DUKE MATHEMATICAL JOURNAL, 1958, 25 (04) : 543 - 552

← 1 2 3 4 5 →