On the almost sure convergence of weighted sums of random elements inD[0,1]
Abstract
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).
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 1981
- Source ID
- 10.1155/s0161171281000574
Entities
People
- C. A. Calhoun
- R. L. Taylor
Organizations
- Air Force Office of Scientific Research
- University of South Carolina