A Weak Law with Random Indices for Randomly Weighted Sums of Rowwise Independent Random Elements in Rademacher Type p Banach Spaces

2002 ◽  
Vol 52 (1-4) ◽  
pp. 85-98 ◽  
Author(s):  
Andrew Rosalsky ◽  
M. Sreehari ◽  
Andrei I. Volodin
Keyword(s):  
Banach Spaces ◽  
Weighted Sums ◽  
Randomly Weighted Sums ◽  
Random Elements ◽  
Rowwise Independent ◽  
Random Indices

scholarly journals Convergence of weighted sums of independent random variables and an extension to Banach space-valued random variables

1979 ◽  
Vol 2 (2) ◽  
pp. 309-323
Author(s):  
W. J. Padgett ◽  
R. L. Taylor
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Real Numbers ◽  
Martingale Theory ◽  
Random Elements ◽  
Schauder Bases

Let{Xk}be independent random variables withEXk=0for allkand let{ank:n≥1, k≥1}be an array of real numbers. In this paper the almost sure convergence ofSn=∑k=1nankXk,n=1,2,…, to a constant is studied under various conditions on the weights{ank}and on the random variables{Xk}using martingale theory. In addition, the results are extended to weighted sums of random elements in Banach spaces which have Schauder bases. This extension provides a convergence theorem that applies to stochastic processes which may be considered as random elements in function spaces.

Stochastic convergence of randomly weighted sums of random elements

1984 ◽  
Vol 2 (3) ◽  
pp. 299-321 ◽  
Author(s):  
Robert Lee Taylor ◽  
Carol Calhoun Raina ◽  
Peter Z. Daffer
Keyword(s):  
Weighted Sums ◽  
Stochastic Convergence ◽  
Randomly Weighted Sums ◽  
Random Elements
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