A spectral representation for max-stable processes. (English) Zbl 0597.60050

de Haan, Laurens

Ann. Probab. 12, 1194-1204 (1984).

Summary: 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.

MSC:

60H05	Stochastic integrals
62M20	Inference from stochastic processes and prediction

Keywords:

spectral representation; max-stable sequence; max-stable process