Limit Properties of Random Variables Associated with a Partial Ordering of $R^d$
Steele, J. Michael
Ann. Probab., Tome 5 (1977) no. 6, p. 395-403 / Harvested from Project Euclid
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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.
Publié le : 1977-06-14
Classification:  Monotone subsequences,  lower layers,  partial ordering,  discrepancy functions,  subadditive processes,  60C05,  60F15,  60K99 
@article{1176995800,
     author = {Steele, J. Michael},
     title = {Limit Properties of Random Variables Associated with a Partial Ordering of $R^d$},
     journal = {Ann. Probab.},
     volume = {5},
     number = {6},
     year = {1977},
     pages = { 395-403},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995800}
}

Steele, J. Michael. Limit Properties of Random Variables Associated with a Partial Ordering of $R^d$. Ann. Probab., Tome 5 (1977) no. 6, pp.  395-403. http://gdmltest.u-ga.fr/item/1176995800/