The Annals of Probability

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

T. Gergley and I. I. Yezhow

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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


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