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

scholarly journals Stability for randomly weighted sums of random elements

1999 ◽  
Vol 22 (3) ◽  
pp. 559-568 ◽  
Author(s):  
Tien-Chung Hu ◽  
Hen-Chao Chang
Keyword(s):  
Banach Space ◽  
Separable Banach Space ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Weighted Sums ◽  
Randomly Weighted Sums ◽  
Random Elements ◽  
Necessary And Sufficient

Let{Xn:n=1,2,3,…}be a sequence of i.i.d. random elements taking values in a separable Banach space of typepand let{An,i:i=1,2,3,…;n=1,2,3,…}be an array of random variables. In this paper, under various assumptions of{An,i}, the necessary and sufficient conditions for∑i=1∞An,iXi→0a.s. are obtained. Also, the necessity of the assumptions of{An,i}is discussed.

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