Stability for randomly weighted sums of random elements

Tien-Chung Hu and Hen-Chao Chang

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-10

Abstract:

Let { X n : n = 1 , 2 , 3 , … } be a sequence of i.i.d. random elements taking values in a separable Banach space of type p and let { A n , i : i = 1 , 2 , 3 , … ; n = 1 , 2 , 3 , … } be an array of random variables. In this paper, under various assumptions of { A n , i } , the necessary and sufficient conditions for ∑ i = 1 ∞ A n , i X i → 0 a.s. are obtained. Also, the necessity of the assumptions of { A n , i } is discussed.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:791210

DOI: 10.1155/S0161171299225598

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