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.
"A Spectral Representation for Max-stable Processes." Ann. Probab. 12 (4) 1194 - 1204, November, 1984. https://doi.org/10.1214/aop/1176993148