Annals of Probability

Limit Properties of Random Variables Associated with a Partial Ordering of $R^d$

J. Michael Steele

Abstract

A limit theorem is established for the length of the longest chain of random values in $R^d$ with respect to a partial ordering. The result is applied to a question raised by T. Robertson and F. T. Wright concerning the generalized empirical distribution function associated with the class of lower layers.

Article information

Source
Ann. Probab., Volume 5, Number 3 (1977), 395-403.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995800

Digital Object Identifier
doi:10.1214/aop/1176995800

Mathematical Reviews number (MathSciNet)
MR438421

Zentralblatt MATH identifier
0381.60010

JSTOR
Steele, J. Michael. Limit Properties of Random Variables Associated with a Partial Ordering of $R^d$. Ann. Probab. 5 (1977), no. 3, 395--403. doi:10.1214/aop/1176995800. https://projecteuclid.org/euclid.aop/1176995800