### Stochastic Compactness of Sample Extremes

Laurens de Haan and Geert Ridder
Source: Ann. Probab. Volume 7, Number 2 (1979), 290-303.

#### Abstract

Let $Y_1, Y_2, \cdots$ be independent and identically distributed random variables with common distribution function $F$ and let $X_n = \max\{Y_1, \cdots, Y_n\}$ for $n = 1, 2, \cdots$. Necessary and sufficient conditions (in terms of $F$) are derived for the existence of a sequence of positive constants $\{a_n\}$ such that the sequence $\{X_n/a_n\}$ is stochastically compact. Moreover, the relation between the stochastic compactness of partial maxima and partial sums of the $Y_n$'s is investigated.

First Page:
Primary Subjects: 60F05
Secondary Subjects: 62G30
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1176995089
JSTOR: links.jstor.org
Digital Object Identifier: doi:10.1214/aop/1176995089
Mathematical Reviews number (MathSciNet): MR525055
Zentralblatt MATH identifier: 0395.60029