## The Annals of Probability

- Ann. Probab.
- Volume 18, Number 2 (1990), 754-789.

### Some Applications of Isoperimetric Methods to Strong Limit Theorems for Sums of Independent Random Variables

#### Abstract

We develop several applications to almost sure limit theorems for sums of independent vector valued random variables of an isoperimetric inequality due to Talagrand. A general treatment of the classical laws of large numbers of Kolmogorov and Prokorov and laws of the iterated logarithm of Kolmogorov and Hartman and Wintner is described. New results as well as simpler new proofs of known ones illustrate the usefulness of isoperimetric methods in this context. We show further how this approach can be used in the study of limit theorems for trimmed sums of independent and identically distributed random variables.

#### Article information

**Source**

Ann. Probab., Volume 18, Number 2 (1990), 754-789.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176990857

**Digital Object Identifier**

doi:10.1214/aop/1176990857

**Mathematical Reviews number (MathSciNet)**

MR1055432

**Zentralblatt MATH identifier**

0713.60005

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)

Secondary: 60F15: Strong theorems

**Keywords**

Isoperimetric inequality law of large numbers law of the iterated logarithm trimming

#### Citation

Ledoux, M.; Talagrand, M. Some Applications of Isoperimetric Methods to Strong Limit Theorems for Sums of Independent Random Variables. Ann. Probab. 18 (1990), no. 2, 754--789. doi:10.1214/aop/1176990857. https://projecteuclid.org/euclid.aop/1176990857