Annals of Probability

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

J. Michael Steele

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60C05: Combinatorial probability
Secondary: 60F15: Strong theorems 60K99: None of the above, but in this section

Keywords
Monotone subsequences lower layers partial ordering discrepancy functions subadditive processes

Citation

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


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