Laws of large numbers for weighted sums of random variables and random elements

1989 ◽  
Vol 5 (2) ◽  
pp. 185-192 ◽  
Author(s):  
Lin Zhengyan
Keyword(s):  
Random Variables ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Sums Of Random Variables ◽  
Large Numbers ◽  
Random Elements

scholarly journals A note on convergence of weighted sums of random variables

1985 ◽  
Vol 8 (4) ◽  
pp. 805-812 ◽  
Author(s):  
Xiang Chen Wang ◽  
M. Bhaskara Rao
Keyword(s):  
Integrability Condition ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Uniform Integrability ◽  
Laws Of Large Numbers ◽  
Sums Of Random Variables ◽  
Large Numbers ◽  
Pairwise Independent Random Variables ◽  
Weak Laws

Under uniform integrability condition, some Weak Laws of large numbers are established for weighted sums of random variables generalizing results of Rohatgi, Pruitt and Khintchine. Some Strong Laws of Large Numbers are proved for weighted sums of pairwise independent random variables generalizing results of Jamison, Orey and Pruitt and Etemadi.

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.

scholarly journals On the almost sure convergence of weighted sums of random elements inD[0,1]

1981 ◽  
Vol 4 (4) ◽  
pp. 745-752
Author(s):  
R. L. Taylor ◽  
C. A. Calhoun
Keyword(s):  
Almost Sure Convergence ◽  
Growth Conditions ◽  
Weighted Sums ◽  
Integral Conditions ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Convergence Results ◽  
Large Numbers ◽  
Random Elements

Let{wn}be a sequence of positive constants andWn=w1+…+wnwhereWn→∞andwn/Wn→∞. Let{Wn}be a sequence of independent random elements inD[0,1]. The almost sure convergence ofWn−1∑k=1nwkXkis established under certain integral conditions and growth conditions on the weights{wn}. The results are shown to be substantially stronger than the weighted sums convergence results of Taylor and Daffer (1980) and the strong laws of large numbers of Ranga Rao (1963) and Daffer and Taylor (1979).

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