## The Annals of Probability

### Some Results on the Cluster Set $C\bigg(\bigg{\frac{S_n}{a_n}\bigg}\bigg)$ and the LIL

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 11, Number 1 (1983), 102-122.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993662

Digital Object Identifier
doi:10.1214/aop/1176993662

Mathematical Reviews number (MathSciNet)
MR682803

Zentralblatt MATH identifier
0507.60002

JSTOR
de Acosta, A.; Kuelbs, J. Some Results on the Cluster Set $C\bigg(\bigg{\frac{S_n}{a_n}\bigg}\bigg)$ and the LIL. Ann. Probab. 11 (1983), no. 1, 102--122. doi:10.1214/aop/1176993662. https://projecteuclid.org/euclid.aop/1176993662