## The Annals of Probability

- Ann. Probab.
- Volume 11, Number 2 (1983), 270-276.

### A New Proof of the Hartman-Wintner Law of the Iterated Logarithm

#### Abstract

A new proof of the Hartman-Wintner law of the iterated logarithm is given. The main new ingredient is a simple exponential inequality. The same method gives a new, simpler proof of a basic result of Kuelbs on the LIL in the Banach space setting.

#### Article information

**Source**

Ann. Probab., Volume 11, Number 2 (1983), 270-276.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176993596

**Digital Object Identifier**

doi:10.1214/aop/1176993596

**Mathematical Reviews number (MathSciNet)**

MR690128

**Zentralblatt MATH identifier**

0512.60014

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60B05: Probability measures on topological spaces

Secondary: 60F05: Central limit and other weak theorems 60F10: Large deviations 60F15: Strong theorems

**Keywords**

Hartman-Wintner law of the iterated logarithm exponential inequality cluster set law of the iterated logarithm in Banach spaces

#### Citation

de Acosta, Alejandro. A New Proof of the Hartman-Wintner Law of the Iterated Logarithm. Ann. Probab. 11 (1983), no. 2, 270--276. doi:10.1214/aop/1176993596. https://projecteuclid.org/euclid.aop/1176993596