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February, 1983 Some Results on the Cluster Set $C\bigg(\bigg{\frac{S_n}{a_n}\bigg}\bigg)$ and the LIL
A. de Acosta, J. Kuelbs
Ann. Probab. 11(1): 102-122 (February, 1983). DOI: 10.1214/aop/1176993662


We investigate the cluster set $C(\{S_n/a_n\})$ under conditions necessary for the bounded law of the iterated logarithm, and obtain necessary and sufficient conditions for the LIL in spaces satisfying a certain comparison principle. In particular, these results settle some previously unanswered questions in the Hilbert space setting.


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A. de Acosta. J. Kuelbs. "Some Results on the Cluster Set $C\bigg(\bigg{\frac{S_n}{a_n}\bigg}\bigg)$ and the LIL." Ann. Probab. 11 (1) 102 - 122, February, 1983.


Published: February, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0507.60002
MathSciNet: MR682803
Digital Object Identifier: 10.1214/aop/1176993662

Primary: 60B05
Secondary: 28C20 , 60B10 , 60B11 , 60B12 , 60F10 , 60F15

Keywords: cluster set , Law of the iterated logarithm , smooth norm spaces , type 2 space , upper Gaussian comparison principle

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 1 • February, 1983
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