Complete convergence for sums of arrays of random elements
Let {Xni} be an array of rowwise independent B-valued random elements and {an} constants such that 0<an↑∞. Under some moment conditions for the array, it is shown that ∑i=1nXni/an converges to 0 completely if and only if ∑i=1nXni/an converges to 0 in probability.
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171200003112 |
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| _version_ | 1832549470584176640 |
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| author | Soo Hak Sung |
| author_facet | Soo Hak Sung |
| author_sort | Soo Hak Sung |
| collection | DOAJ |
| description | Let {Xni} be an array of rowwise independent B-valued
random elements and {an} constants such that
0<an↑∞. Under some moment conditions for the array,
it is shown that ∑i=1nXni/an converges to 0 completely if and only if ∑i=1nXni/an converges to
0 in probability. |
| format | Article |
| id | doaj-art-c35988f98ebf491d9bfeab28e4bc1f53 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c35988f98ebf491d9bfeab28e4bc1f532025-02-03T06:11:21ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-01231178979410.1155/S0161171200003112Complete convergence for sums of arrays of random elementsSoo Hak Sung0Department of Applied Mathematics, Pai Chai University, Taejon 302-735, South KoreaLet {Xni} be an array of rowwise independent B-valued random elements and {an} constants such that 0<an↑∞. Under some moment conditions for the array, it is shown that ∑i=1nXni/an converges to 0 completely if and only if ∑i=1nXni/an converges to 0 in probability.http://dx.doi.org/10.1155/S0161171200003112 |
| spellingShingle | Soo Hak Sung Complete convergence for sums of arrays of random elements International Journal of Mathematics and Mathematical Sciences |
| title | Complete convergence for sums of arrays of random elements |
| title_full | Complete convergence for sums of arrays of random elements |
| title_fullStr | Complete convergence for sums of arrays of random elements |
| title_full_unstemmed | Complete convergence for sums of arrays of random elements |
| title_short | Complete convergence for sums of arrays of random elements |
| title_sort | complete convergence for sums of arrays of random elements |
| url | http://dx.doi.org/10.1155/S0161171200003112 |
| work_keys_str_mv | AT soohaksung completeconvergenceforsumsofarraysofrandomelements |