## The Annals of Probability

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

### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1214/aop/1176996399

**Mathematical Reviews number (MathSciNet)**

MR372993

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60G50: Sums of independent random variables; random walks

Secondary: 60I15 60F99: None of the above, but in this section

**Keywords**

Maximum distribution of sums of independent random variables random walk

#### Citation

Gergley, T.; Yezhow, I. I. On the Distribution of the Maximum of the Sequence of Sums of Independent Random Variables. Ann. Probab. 3 (1975), no. 2, 289--297. doi:10.1214/aop/1176996399. https://projecteuclid.org/euclid.aop/1176996399