scholarly journals On the application of strong approximation to weak convergence of products of sums for dependent random variables

2008 ◽  
Vol 11 (4) ◽  
pp. 749
Author(s):  
Matuła ◽  
Stępień
Keyword(s):  
Weak Convergence ◽  
Strong Approximation ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Products Of Sums

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.

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].

Weak convergence of the adjusted range of cumulative sums of exchangeable random variables

1983 ◽  
Vol 20 (02) ◽  
pp. 297-304 ◽  
Author(s):  
Brent M. Troutman
Keyword(s):  
Weak Convergence ◽  
Asymptotic Distribution ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Random Functions ◽  
Exchangeable Random Variables ◽  
Convergence Results ◽  
Cumulative Sums

Let be the adjusted range of the cumulative sums of a sequence , where . Weak convergence results for random functions constructed from cumulative sums of {Xs } are used to obtain the asymptotic distribution and moments of when {Xs } are exchangeable, or symmetrically dependent, random variables.

Weak convergence of the adjusted range of cumulative sums of exchangeable random variables

1983 ◽  
Vol 20 (2) ◽  
pp. 297-304 ◽  
Author(s):  
Brent M. Troutman
Keyword(s):  
Weak Convergence ◽  
Asymptotic Distribution ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Random Functions ◽  
Exchangeable Random Variables ◽  
Convergence Results ◽  
Cumulative Sums

Let be the adjusted range of the cumulative sums of a sequence , where . Weak convergence results for random functions constructed from cumulative sums of {Xs} are used to obtain the asymptotic distribution and moments of when {Xs} are exchangeable, or symmetrically dependent, random variables.

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.

Sign in / Sign up

Export Citation Format

Share Document