A strong law for $B$-valued arrays
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- by De Li Li, M. Bhaskara Rao and R. J. Tomkins PDF
- Proc. Amer. Math. Soc. 123 (1995), 3205-3212 Request permission
Abstract:
Let $(B,\left \| \bullet \right \|)$ be a real separable Banach space and $\{ {X_{n,k}};n \geq 1,1 \leq k \leq n\}$ a triangular array of iid B-valued random variables. Set $S(n) = \sum \nolimits _{k = 1}^n {{X_{n,k}},n \geq 1}$, and ${\operatorname {Log}} t = \log \max \{ e,t\} ,t \in \Re$. In this paper, we characterize the limit behavior of $S(n)/\sqrt {2n {\operatorname {Log}} n} ,n \geq 1$. As an application of our result, we resolve an open problem posed by Hu and Weber (1992). The case of row-wise independent arrays is also dealt with.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3205-3212
- MSC: Primary 60B12; Secondary 60F15
- DOI: https://doi.org/10.1090/S0002-9939-1995-1291783-8
- MathSciNet review: 1291783