## The Annals of Probability

### On the Distribution of the Maximum of the Sequence of Sums of Independent Random Variables

#### Abstract

Let $\xi_1, \xi_2, \cdots$ be independent random variables. The distribution of $\max (0, \xi_1, \xi_1 + \xi_2, \cdots, \xi_1 + \cdots + \xi_n)$ is investigated by means of a method based on the construction of certain events with easily determined proabilities. These yield a new formula for the distribution of the maximum which is sometimes more useful than that given in literature.

#### Article information

Source
Ann. Probab., Volume 3, Number 2 (1975), 289-297.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996399

Digital Object Identifier
doi:10.1214/aop/1176996399

Mathematical Reviews number (MathSciNet)
MR372993

JSTOR