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Convergence of series of scalar- and vector-valued random variables and a subsequence principle in $ L\sb 2$

Author: S. J. Dilworth
Journal: Trans. Amer. Math. Soc. 301 (1987), 375-384
MSC: Primary 60B12; Secondary 60G42
MathSciNet review: 879579
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Abstract: Let $ ({d_n})_{n = 1}^\infty $ be a martingale difference sequence in $ {L_0}(X)$, where $ X$ is a uniformly convex Banach space. We investigate a necessary condition for convergence of the series $ \sum {_{n = 1}^\infty {a_n}{d_n}} $. We also prove a related subsequence principle for the convergence of a series of square-integrable scalar random variables.

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Keywords: Martingale, uniformly convex, subsequence
Article copyright: © Copyright 1987 American Mathematical Society