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April, 1989 The Law of the Iterated Logarithm for $B$-Valued Random Variables with Multidimensional Indices
Deli Li, Zhiquan Wu
Ann. Probab. 17(2): 760-774 (April, 1989). DOI: 10.1214/aop/1176991425

Abstract

Given independent identically distributed random variables $\{X, X_{\bar{n}}; \bar{n} \in \mathbb{N}^d\}$ indexed by $d$-tuples of positive integers and taking values in a separable Banach space $B$ we approximate the rectangular sums $\{\sum_{\bar{k}} \leq \bar{n} X_{\bar{k}}; \bar{n} \in \mathbb{N}^d\}$ by a Brownian sheet and obtain necessary and sufficient conditions for $X$ to satisfy, respectively, the bounded, compact and functional law of the iterated logarithm when $d \geq 2$. These results improve, in particular, the previous work by Morrow [17].

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Deli Li. Zhiquan Wu. "The Law of the Iterated Logarithm for $B$-Valued Random Variables with Multidimensional Indices." Ann. Probab. 17 (2) 760 - 774, April, 1989. https://doi.org/10.1214/aop/1176991425

Information

Published: April, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0679.60007
MathSciNet: MR985388
Digital Object Identifier: 10.1214/aop/1176991425

Subjects:
Primary: 60B12
Secondary: 60F15

Keywords: Brownian sheet , central limit theorem , Law of the iterated logarithm , pre-Gaussian

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 2 • April, 1989
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