## The Annals of Probability

- Ann. Probab.
- Volume 7, Number 6 (1979), 1078-1081.

### Rapidly Growing Random Walks and an Associated Stopping Time

#### Abstract

An exponential limit distribution is obtained for stopping times associated with partial sums of independent, identically distributed random variables whose distribution function is slowly varying at infinity. It is also demonstrated that a generalized law of the iterated logarithm cannot obtain in such a case.

#### Article information

**Source**

Ann. Probab., Volume 7, Number 6 (1979), 1078-1081.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176994903

**Digital Object Identifier**

doi:10.1214/aop/1176994903

**Mathematical Reviews number (MathSciNet)**

MR548904

**Zentralblatt MATH identifier**

0424.60024

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F05: Central limit and other weak theorems

Secondary: 60F15: Strong theorems

**Keywords**

Random walk stopping time slowly varying generalized law of the iterated logarithm

#### Citation

Teicher, Henry. Rapidly Growing Random Walks and an Associated Stopping Time. Ann. Probab. 7 (1979), no. 6, 1078--1081. doi:10.1214/aop/1176994903. https://projecteuclid.org/euclid.aop/1176994903