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Limit theorems for randomly weighted sums of random elements in normed linear spaces

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  • Cabrera, M. Ordóñez

Abstract

Let {Vn; n >= 1} be a sequence of random elements in a separable normed linear space E, uniformly dominated by a random variable V. Let {Ank; K = 1, 2, ..., n; n >= 1} be a triangular array of random variables. In this paper, conditions for the convergence of [Sigma]k=1n AnkVk to zero (in probability and completely) are obtained. No geometric condition on E is imposed.

Suggested Citation

  • Cabrera, M. Ordóñez, 1988. "Limit theorems for randomly weighted sums of random elements in normed linear spaces," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 139-145, April.
    • Handle: RePEc:eee:jmvana:v:25:y:1988:i:1:p:139-145
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    Cited by:

    1. Hu, Tien-Chung & Cabrera, Manuel Ordóñez & Volodin, Andrei I., 2001. "Convergence of randomly weighted sums of Banach space valued random elements and uniform integrability concerning the random weights," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 155-164, January.
    2. Rosalsky, Andrew & Sreehari, M., 1998. "On the limiting behavior of randomly weighted partial sums," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 403-410, November.

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