Some Examples of the Weak and Strong Laws of Large Numbers for Averages of Mutually Independent Random Variables

1978 ◽  
Vol 32 (1) ◽  
pp. 34-36
Author(s):  
Nancy L. Geller
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Mutually Independent

scholarly journals On the strong law for arrays and for the bootstrap mean and variance

1997 ◽  
Vol 20 (2) ◽  
pp. 375-382 ◽  
Author(s):  
Tien-Chung Hu ◽  
R. L. Taylor
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Interesting Application ◽  
Strong Law ◽  
Moment Conditions ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Mean And Variance ◽  
Rowwise Independent

Chung type strong laws of large numbers are obtained for arrays of rowwise independent random variables under various moment conditions. An interesting application of these results is the consistency of the bootstrap mean and variance.

scholarly journals On Chung-Teicher type strong law for arrays of vector-valued random variables

2004 ◽  
Vol 2004 (9) ◽  
pp. 443-458
Author(s):  
Anna Kuczmaszewska
Keyword(s):  
Banach Space ◽  
Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Random Elements ◽  
Vector Valued

We study the equivalence between the weak and strong laws of large numbers for arrays of row-wise independent random elements with values in a Banach spaceℬ. The conditions under which this equivalence holds are of the Chung or Chung-Teicher types. These conditions are expressed in terms of convergence of specific series ando(1)requirements on specific weighted row-wise sums. Moreover, there are not any conditions assumed on the geometry of the underlying Banach space.

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