## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 40, Number 2 (1969), 681-687.

### Inequalities with Applications to the Weak Convergence of Random Processes with Multi-Dimensional Time Parameters

#### Abstract

Bounds on the distribution of the maximum of the absolute values of the "partial sums" constructed from a multi-dimensional array of independent random variables are derived and used to establish the weak convergence of certain random functions defined in terms of such "partial sums".

#### Article information

**Source**

Ann. Math. Statist., Volume 40, Number 2 (1969), 681-687.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177697741

**Digital Object Identifier**

doi:10.1214/aoms/1177697741

**Mathematical Reviews number (MathSciNet)**

MR246359

**Zentralblatt MATH identifier**

0214.17701

**JSTOR**

links.jstor.org

#### Citation

Wichura, Michael J. Inequalities with Applications to the Weak Convergence of Random Processes with Multi-Dimensional Time Parameters. Ann. Math. Statist. 40 (1969), no. 2, 681--687. doi:10.1214/aoms/1177697741. https://projecteuclid.org/euclid.aoms/1177697741