Open Access
June, 1976 On Weak Convergence of Extremal Processes
Ishay Weissman
Ann. Probab. 4(3): 470-473 (June, 1976). DOI: 10.1214/aop/1176996096


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.


Download Citation

Ishay Weissman. "On Weak Convergence of Extremal Processes." Ann. Probab. 4 (3) 470 - 473, June, 1976.


Published: June, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0401.60058
MathSciNet: MR400330
Digital Object Identifier: 10.1214/aop/1176996096

Primary: 60B10
Secondary: 60G99

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

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 3 • June, 1976
Back to Top