On Chung-Teicher type strong law for arrays of vector-valued random variables
We study the equivalence between the weak and strong laws of large numbers for arrays of row-wise independent random elements with values in a Banach space ℬ. The conditions under which this equivalence holds are of the Chung or Chung-Teicher types. These conditions are expressed in terms of converg...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204301031 |
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| Summary: | We study the equivalence between the weak and strong laws of
large numbers for arrays of row-wise independent random elements
with values in a Banach space ℬ. The conditions
under which this equivalence holds are of the Chung or
Chung-Teicher types. These conditions are expressed in terms of
convergence of specific series and o(1) requirements on
specific weighted row-wise sums. Moreover, there are not any
conditions assumed on the geometry of the underlying Banach space. |
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| ISSN: | 0161-1712 1687-0425 |