The Annals of Probability

A Spectral Representation for Max-stable Processes

L. De Haan

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Abstract

The elements of an arbitrary max-stable sequence are exhibited as functionals of a 2-dimensional Poisson point process. The result is extended to a continuous time max-stable process that is continuous in probability. We define an analogue of a stochastic integral appropriate for this context.

Article information

Source
Ann. Probab., Volume 12, Number 4 (1984), 1194-1204.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993148

Digital Object Identifier
doi:10.1214/aop/1176993148

Mathematical Reviews number (MathSciNet)
MR757776

Zentralblatt MATH identifier
0597.60050

JSTOR
links.jstor.org

Subjects
Primary: 60H05: Stochastic integrals
Secondary: 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]

Keywords
Max-stability spectral representation

Citation

Haan, L. De. A Spectral Representation for Max-stable Processes. Ann. Probab. 12 (1984), no. 4, 1194--1204. doi:10.1214/aop/1176993148. https://projecteuclid.org/euclid.aop/1176993148


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