WITHDRAWN: Convergence of weighted averages of pairwise independent random variables

2008 ◽  
Author(s):  
Katusi Fukuyama ◽  
Dinesh Neupane
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Averages ◽  
Pairwise Independent Random Variables

scholarly journals Complete convergence for weighted sums of pairwise independent random variables

2017 ◽  
Vol 15 (1) ◽  
pp. 467-476
Author(s):  
Li Ge ◽  
Sanyang Liu ◽  
Yu Miao
Keyword(s):  
Rate Of Convergence ◽  
Complete Convergence ◽  
Moving Average ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Pairwise Independent Random Variables ◽  
Moving Average Processes

Abstract In the present paper, we have established the complete convergence for weighted sums of pairwise independent random variables, from which the rate of convergence of moving average processes is deduced.

scholarly journals Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables

1999 ◽  
Vol 22 (1) ◽  
pp. 171-177 ◽  
Author(s):  
Dug Hun Hong ◽  
Seok Yoon Hwang
Keyword(s):  
Law Of Large Numbers ◽  
Double Sequence ◽  
Random Variables ◽  
Independent Random Variables ◽  
Real Numbers ◽  
Strong Law ◽  
One Dimensional ◽  
Large Numbers ◽  
Pairwise Independent Random Variables ◽  
The One

Let {Xij}be a double sequence of pairwise independent random variables. If P{|Xmn|≥t}≤P{|X|≥t}for all nonnegative real numbers tandE|X|p(log+|X|)3<∞, for1<p<2, then we prove that∑i=1m∑j=1n(Xij−EXij)(mn)1/p→0    a.s.   as  m∨n→∞.                                     (0.1)Under the weak condition ofE|X|plog+|X|<∞, it converges to 0inL1. And the results can be generalized to anr-dimensional array of random variables under the conditionsE|X|p(log+|X|)r+1<∞,E|X|p(log+|X|)r−1<∞, respectively, thus, extending Choi and Sung's result [1] of the one-dimensional case.

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