## The Annals of Probability

### Variational Inequalities with Examples and an Application to the Central Limit Theorem

#### Abstract

Upper bounds for the distance in variation between an arbitrary probability measure and the standard normal one are established via some integrodifferential functionals including information. The results are illustrated by gamma- and $t$-distributions. Moreover, as a by-product, another proof of the central limit theorem is obtained.

#### Article information

Source
Ann. Probab., Volume 22, Number 3 (1994), 1607-1618.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176988616

Digital Object Identifier
doi:10.1214/aop/1176988616

Mathematical Reviews number (MathSciNet)
MR1303658

Zentralblatt MATH identifier
0835.60023

JSTOR