On the almost sure convergence of weighted sums of random elements in D[0,1]
Let {wn} be a sequence of positive constants and Wn=w1+…+wn where Wn→∞ and wn/Wn→∞. Let {Wn} be a sequence of independent random elements in D[0,1]. The almost sure convergence of Wn−1∑k=1nwkXk is established under certain integral conditions and growth conditions on the weights {wn}. The results ar...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
Hindawi Limited
1981-01-01
|
Series: | International Journal of Mathematics and Mathematical Sciences |
Subjects: | |
Online Access: | http://dx.doi.org/10.1155/S0161171281000574 |