Date of this Version
The Annals of Probability
A limit theorem is established for the length of the longest chain of random values in Rd 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.
The original and published work is available at: https://projecteuclid.org/euclid.aop/1176995800#abstract
monotone subsequences, lower layers, partial ordering, discrepancy functions, subadditive processes
Steele, J. M. (1977). Limit Properties of Random Variables Associated With a Partial Ordering of Rd. The Annals of Probability, 5 (3), 395-403. http://dx.doi.org/10.1214/aop/1176995800
Date Posted: 27 November 2017
This document has been peer reviewed.