## The Annals of Probability

### Sharper Bounds for Gaussian and Empirical Processes

M. Talagrand

#### Abstract

Under natural conditions on a class $\mathscr{F}$ of functions on a probability space, near optimal bounds are given for the probabilities $P\big(\sup_{f\in\mathscr{F}}|\sum_{i\leq n} f(X_i) - nE(f)| \geq M\sqrt n\big)$. The method is a variation of this author's method to study the tail probability of the supremum of a Gaussian process.

#### Article information

Source
Ann. Probab., Volume 22, Number 1 (1994), 28-76.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176988847

Digital Object Identifier
doi:10.1214/aop/1176988847

Mathematical Reviews number (MathSciNet)
MR1258865

Zentralblatt MATH identifier
0798.60051

JSTOR