Strong laws of large numbers for arrays of rowwise independent random elements
Let {Xnk} be an array of rowwise independent random elements in a separable Banach space of type p+δ with EXnk=0 for all k, n. The complete convergence (and hence almost sure convergence) of n−1/p∑k=1nXnk to 0, 1≤p<2, is obtained when {Xnk} are uniformly bounded by a random variable X with E|X|2p...
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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171287000899 |
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| _version_ | 1832545489825824768 |
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| author | Robert Lee Taylor Tien-Chung Hu |
| author_facet | Robert Lee Taylor Tien-Chung Hu |
| author_sort | Robert Lee Taylor |
| collection | DOAJ |
| description | Let {Xnk} be an array of rowwise independent random elements in a separable
Banach space of type p+δ with EXnk=0 for all k, n. The complete convergence (and hence almost sure convergence) of n−1/p∑k=1nXnk to 0, 1≤p<2, is obtained when {Xnk} are uniformly bounded by a random variable X with E|X|2p<∞. When the array {Xnk} consists of i.i.d, random elements, then it is shown that n−1/p∑k=1nXnk converges completely to 0 if and only if E‖X11‖2p<∞. |
| format | Article |
| id | doaj-art-25346ee69a604e5e98c7f1c4e6bc0e00 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-25346ee69a604e5e98c7f1c4e6bc0e002025-02-03T07:25:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110480581410.1155/S0161171287000899Strong laws of large numbers for arrays of rowwise independent random elementsRobert Lee Taylor0Tien-Chung Hu1Depatment of statistics , University of Georgia, Athens, GA 30602, USADepatment of Mathematics, National Tsing-Hua University, Hsin-chu, TaiwanLet {Xnk} be an array of rowwise independent random elements in a separable Banach space of type p+δ with EXnk=0 for all k, n. The complete convergence (and hence almost sure convergence) of n−1/p∑k=1nXnk to 0, 1≤p<2, is obtained when {Xnk} are uniformly bounded by a random variable X with E|X|2p<∞. When the array {Xnk} consists of i.i.d, random elements, then it is shown that n−1/p∑k=1nXnk converges completely to 0 if and only if E‖X11‖2p<∞.http://dx.doi.org/10.1155/S0161171287000899random elementsstrong laws of large numberscomplete convergence Rademacher type p+δ spaces. |
| spellingShingle | Robert Lee Taylor Tien-Chung Hu Strong laws of large numbers for arrays of rowwise independent random elements International Journal of Mathematics and Mathematical Sciences random elements strong laws of large numbers complete convergence Rademacher type p+δ spaces. |
| title | Strong laws of large numbers for arrays of rowwise independent random elements |
| title_full | Strong laws of large numbers for arrays of rowwise independent random elements |
| title_fullStr | Strong laws of large numbers for arrays of rowwise independent random elements |
| title_full_unstemmed | Strong laws of large numbers for arrays of rowwise independent random elements |
| title_short | Strong laws of large numbers for arrays of rowwise independent random elements |
| title_sort | strong laws of large numbers for arrays of rowwise independent random elements |
| topic | random elements strong laws of large numbers complete convergence Rademacher type p+δ spaces. |
| url | http://dx.doi.org/10.1155/S0161171287000899 |
| work_keys_str_mv | AT robertleetaylor stronglawsoflargenumbersforarraysofrowwiseindependentrandomelements AT tienchunghu stronglawsoflargenumbersforarraysofrowwiseindependentrandomelements |