A convergence theorem for sums of dependent Hilbert space valued triangular arrays
β Scribed by Li Zezhi; Zhang Buchen
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 178 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0167-7152
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π 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
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For weighted sums of the form Sn = Ejknl anj (Vnj--Cnj) where {anj, 1 <<.j<~kn < oo, n~> 1} are constants, {V~j, 1 <~j<~k~, n>~l} are random elements in a real separable martingale type p Banach space, and {cnj, 1 <<.j<~kn, n>>-1} are suitable conditional expectations, a mean convergence theorem and