The Annals of Probability

Records in a Partially Ordered Set

Charles M. Goldie and Sidney Resnick

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Abstract

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.

Article information

Source
Ann. Probab., Volume 17, Number 2 (1989), 678-699.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991421

Digital Object Identifier
doi:10.1214/aop/1176991421

Mathematical Reviews number (MathSciNet)
MR985384

Zentralblatt MATH identifier
0678.60001

JSTOR
links.jstor.org

Subjects
Primary: 60B05: Probability measures on topological spaces
Secondary: 60K99: None of the above, but in this section 06A10

Keywords
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

Citation

Goldie, Charles M.; Resnick, Sidney. Records in a Partially Ordered Set. Ann. Probab. 17 (1989), no. 2, 678--699. doi:10.1214/aop/1176991421. https://projecteuclid.org/euclid.aop/1176991421


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