The Annals of Probability

On Weak Convergence of Extremal Processes

Ishay Weissman

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Abstract

Lamperti in 1964 showed that the convergence of the marginals of an extremal process generated by independent and identically distributed random variables implies the full weak convergence in the Skorohod $J_1$-topology. This result is generalized to the $k$th extremal process and to random variables which need not be identically distributed. The proof here is based on the weak convergence of a certain point-process (which counts the number of up-crossings of the variables) to a two-dimensional nonhomogeneous Poisson process.

Article information

Source
Ann. Probab., Volume 4, Number 3 (1976), 470-473.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996096

Digital Object Identifier
doi:10.1214/aop/1176996096

Mathematical Reviews number (MathSciNet)
MR400330

Zentralblatt MATH identifier
0401.60058

JSTOR
links.jstor.org

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60G99: None of the above, but in this section

Keywords
Extremal processes multivariate $k$-dimensional extremal processes nonhomogeneous two-dimensional Poisson process $D\lbrack a, b \rbrack$ space Skorohod space of functions with several parameters weak convergence

Citation

Weissman, Ishay. On Weak Convergence of Extremal Processes. Ann. Probab. 4 (1976), no. 3, 470--473. doi:10.1214/aop/1176996096. https://projecteuclid.org/euclid.aop/1176996096


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