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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1981-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171281000574 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849412625717264384 |
|---|---|
| author | R. L. Taylor C. A. Calhoun |
| author_facet | R. L. Taylor C. A. Calhoun |
| author_sort | R. L. Taylor |
| collection | DOAJ |
| description | 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 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). |
| format | Article |
| id | doaj-art-5f39ac80488f4d1e89a8e188680fea8a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1981-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5f39ac80488f4d1e89a8e188680fea8a2025-08-20T03:34:22ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-014474575210.1155/S0161171281000574On the almost sure convergence of weighted sums of random elements in D[0,1]R. L. Taylor0C. A. Calhoun1Department of Mathematics and Statistics, University of South Carolina, Columbia, S. C. 29208, USADepartment of Mathematics and Statistics, University of South Carolina, Columbia, S. C. 29208, USALet {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 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).http://dx.doi.org/10.1155/S0161171281000574weighted sumsrandom elements in D[{0,1}] strong laws of large numbersintegral conditionsand almost sure convergence. |
| spellingShingle | R. L. Taylor C. A. Calhoun On the almost sure convergence of weighted sums of random elements in D[0,1] International Journal of Mathematics and Mathematical Sciences weighted sums random elements in D[{0,1}] strong laws of large numbers integral conditions and almost sure convergence. |
| title | On the almost sure convergence of weighted sums of random elements in D[0,1] |
| title_full | On the almost sure convergence of weighted sums of random elements in D[0,1] |
| title_fullStr | On the almost sure convergence of weighted sums of random elements in D[0,1] |
| title_full_unstemmed | On the almost sure convergence of weighted sums of random elements in D[0,1] |
| title_short | On the almost sure convergence of weighted sums of random elements in D[0,1] |
| title_sort | on the almost sure convergence of weighted sums of random elements in d 0 1 |
| topic | weighted sums random elements in D[{0,1}] strong laws of large numbers integral conditions and almost sure convergence. |
| url | http://dx.doi.org/10.1155/S0161171281000574 |
| work_keys_str_mv | AT rltaylor onthealmostsureconvergenceofweightedsumsofrandomelementsind01 AT cacalhoun onthealmostsureconvergenceofweightedsumsofrandomelementsind01 |