Limit Theorems for Random Elements in Ideals of Order-Bounded Elements of Functional Banach Lattices
✍ Scribed by I. K. Matsak; A. M. Plichko
- Book ID
- 110291816
- Publisher
- Springer
- Year
- 2001
- Tongue
- English
- Weight
- 117 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0041-5995
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
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
1) a{.) denotes the smallest a-algebra generated by the RV's in braces.
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