Records in a Partially Ordered Set

Goldie, Charles M. ; Resnick, Sidney

Ann. Probab., Tome 17 (1989) no. 4, p. 678-699 / Harvested from Project Euclid

Résumé

We consider independent identically distributed observations taking values in a general partially ordered set. Under no more than a necessary measurability condition we develop a theory of record values analogous to parts of the well-known theory of real records, and discuss its application to many partially ordered topological spaces. In the particular case of $\mathbb{R}^2$ under a componentwise partial order, assuming the underlying distribution of the observations to be in the domain of attraction of an extremal law, we give a criterion for there to be infinitely many records.

Détail

Publié le : 1989-04-14
Classification:  Bivariate extremal law,  continuous lattice,  Fell topology,  hazard measure,  lattice,  Lawson topology,  partially ordered set,  random closed set,  records,  semicontinuity,  sup vague topology,  upper semicontinuity,  60B05,  60K99,  06A10