scholarly journals Weak and Almost Sure Convergence for Products of Sums of Associated Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Przemyslaw Matula ◽  
Iwona Stepien
Keyword(s):  
Weak Convergence ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Stationary Sequences ◽  
Associated Random Variables ◽  
Products Of Sums ◽  
Normal Law ◽  
Log Normal

We study weak convergence of product of sums of stationary sequences of associated random variables to the log-normal law. The almost sure version of this result is also presented. The obtained theorems extend and generalize some of the results known so far for independent or associated random variables.

SOME LIMITING BEHAVIOR FOR ASYMPTOTICALLY NEGATIVE ASSOCIATED RANDOM VARIABLES

2016 ◽  
Vol 32 (1) ◽  
pp. 58-66 ◽  
Author(s):  
Qunying Wu ◽  
Yuanying Jiang
Keyword(s):  
Convergence Theorem ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Independent Random Variables ◽  
Strong Law ◽  
Limiting Behavior ◽  
Associated Random Variables ◽  
Large Numbers

In this paper, we study the almost sure convergence for sequences of asymptotically negative associated (ANA) random variables. As a result, we extend the classical Khintchine–Kolmogorov convergence theorem, Marcinkiewicz strong law of large numbers, and the three series theorem for sequences of independent random variables to sequences of ANA random variables without necessarily adding any extra conditions.

scholarly journals Functional Limit Theorem for Products of Sums of Independent and Nonidentically Distributed Random Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Przemysław Matuła ◽  
Iwona Stępień
Keyword(s):  
Limit Theorem ◽  
Weak Convergence ◽  
Limit Theorems ◽  
Random Variables ◽  
Functional Limit Theorem ◽  
Functional Limit ◽  
Generalize Limit ◽  
Products Of Sums

We study the weak convergence in the spaceD[0,1]of processes constructed from products of sums of independent but not necessarily identically distributed random variables. The presented results extend and generalize limit theorems known so far for i.i.d. sequences.

On the Almost sure Convergence Rate for Weighted Sums of Negatively Associated Random Variables with Application to Priestley-Chao Estimate

2015 ◽  
Vol 742 ◽  
pp. 449-452
Author(s):  
Gan Ji Huang ◽  
Guo Dong Xing
Keyword(s):  
Convergence Rate ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Weighted Sums ◽  
Exponential Inequality ◽  
Regression Estimate ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Negatively Associated Random Variables ◽  
Existing Result

This paper deals with the problem of almost sure convergence rate for weighted sums of negatively associated random variables. A new convergence rate is obtained base on an exponential inequality, the result obtained extends and has a fast convergence rate compare with the existing result. As an application, we study the Priestley-Chao estimate of nonparametric regression estimate and the convergence rate is derived.

scholarly journals Weak convergence of product of sums of independent variables with missing values

Filomat ◽  
2010 ◽  
Vol 24 (3) ◽  
pp. 73-81
Author(s):  
Ivana Ilic
Keyword(s):  
Weak Convergence ◽  
Missing Values ◽  
Random Variables ◽  
Independent Variables ◽  
Products Of Sums ◽  
Incomplete Sample

Let (Xn) be a sequence of independent and non-identically distributed random variables. We assume that only observations of (Xn) at certain points are available. We study limit properties in the sense of weak convergence in the space D[0,1] of certain processes based on an incomplete sample from {X1, X2 ...,Xn }. This is an extension of the results of Matula and Stepien [2009. Weak convergence of products of sums of independent and non-identically distributed random variables. J. Math. Anal. Appl. 353, 49-54].

scholarly journals On exact strong laws of large numbers under general dependence conditions

2018 ◽  
Vol 38 (1) ◽  
pp. 103-121 ◽  
Author(s):  
André Adler ◽  
Przemysław Matuła
Keyword(s):  
Random Variables ◽  
Almost Sure Convergence ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Laws Of Large Numbers ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Strong Laws ◽  
Large Numbers ◽  
Dependence Conditions

We study the almost sure convergence of weighted sums of dependent random variables to a positive and finite constant, in the case when the random variables have either mean zero or no mean at all. These are not typical strong laws and they are called exact strong laws of large numbers. We do not assume any particular type of dependence and furthermore consider sequences which are not necessarily identically distributed. The obtained results may be applied to sequences of negatively associated random variables.

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