scholarly journals MEAN CONVERGENCE THEOREMS AND WEAK LAWS OF LARGE NUMBERS FOR DOUBLE ARRAYS OF RANDOM ELEMENTS IN BANACH SPACES

2010 ◽  
Vol 47 (3) ◽  
pp. 467-482 ◽  
Author(s):  
Le Van Dung ◽  
Nguyen Duy Tien
Keyword(s):  
Banach Spaces ◽  
Convergence Theorems ◽  
Laws Of Large Numbers ◽  
Mean Convergence ◽  
Large Numbers ◽  
Random Elements ◽  
Weak Laws

scholarly journals Mean convergence theorems and weak laws of large numbers for double arrays of random variables

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Le Van Thanh
Keyword(s):  
Positive Integer ◽  
Random Variables ◽  
Convergence Theorems ◽  
Laws Of Large Numbers ◽  
Mean Convergence ◽  
Convergence Results ◽  
Large Numbers ◽  
The Mean ◽  
Weak Laws ◽  
Positive Integers

For a double array of random variables {Xmn, m ≥ 1, n ≥ 1}, mean convergence theorems and weak laws of large numbers are established. For the mean convergence results, conditions are provided under which ∑i=1km∑j=1lnamnij(Xij−EXij)→Lr0(0<r≤2) where {amnij;m,n,i,j≥1} are constants, and {kn,n≥1} and {ln,n≥1} are sequences of positive integers. The weak law results provide conditions for ∑i=1Tm∑j=1τnamnij(Xij−EXij)→p0 to hold where {Tm,m≥1} and {τn,n≥1} are sequences of positive integer-valued random variables. The sharpness of the results is illustrated by examples.

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