## The Annals of Probability

- Ann. Probab.
- Volume 9, Number 3 (1981), 377-394.

### When is the Cluster Set of $S_n/a_n$ Empty?

#### Abstract

We investigate the relationship between the bounded law of the iterated logarithm and the compact law of the iterated logarithm for Banach space valued random variables through the cluster set of $S_n/a_n$. Some rate of escape questions are also examined.

#### Article information

**Source**

Ann. Probab., Volume 9, Number 3 (1981), 377-394.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176994412

**Digital Object Identifier**

doi:10.1214/aop/1176994412

**Mathematical Reviews number (MathSciNet)**

MR614624

**Zentralblatt MATH identifier**

0459.60005

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60B05: Probability measures on topological spaces

Secondary: 60B10: Convergence of probability measures 60F10: Large deviations 28A40

**Keywords**

Law of the iterated logarithm cluster set central limit theorem rates of escape

#### Citation

Kuelbs, J. When is the Cluster Set of $S_n/a_n$ Empty?. Ann. Probab. 9 (1981), no. 3, 377--394. doi:10.1214/aop/1176994412. https://projecteuclid.org/euclid.aop/1176994412