Convergence of randomly weighted sums of Banach-space-valued random elements under some conditions of uniform integrability
✍ Scribed by M. Ordóñez Cabrera; A. Volodin
- Publisher
- Springer US
- Year
- 2006
- Tongue
- English
- Weight
- 145 KB
- Volume
- 138
- Category
- Article
- ISSN
- 1573-8795
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📜 SIMILAR VOLUMES
We obtain complete convergence results for arrays of rowwise independent Banach space valued random elements. In the main result no assumptions are made concerning the geometry of the underlying Banach space. As corollaries we obtain a result on complete convergence in stable type p Banach spaces an
The notion of conditional compactly uniform pth-order integrability of an array of random elements in a separable Banach space concerning an array of random variables and relative to a sequence of -algebras is introduced and characterized. We state a conditional law for randomly weighted sums of ran
For a sequence of Banach space valued random elements {Vn; n¿1} (which are not necessarily independent) with the series ∞ n = 1 Vn converging unconditionally in probability and an inÿnite array a = {ani; i¿n; n¿1} of constants, conditions are given under which (i) for all n¿1, the sequence of weight