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On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving average processes

✍ Scribed by S.Ejaz Ahmed; Rita Giuliano Antonini; Andrei Volodin

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
112 KB
Volume
58
Category
Article
ISSN
0167-7152

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✦ Synopsis

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 and on the complete convergence of moving average processes.

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✍ Tien-Chung Hu; Eunwoo Nam; Andrew Rosalsky; Andrei I. Volodin 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 95 KB

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