Extremal stochastic integrals: a parallel between max-stable processes and α-stable processes

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Spectral representations of sum- and max-stable processes (2009, background): “Now we reprove the following result of de Haan and Pickands (1986) (see also Stoev and Taqqu (2005) for the slightly more general version given below).”
On the structure and representations of max-stable processes (2009, methodology): “2 of [34], to establish (ii), we should show that any measurable α-Fréchet process X satisfies Condition S.”
On the ergodicity and mixing of max-stable processes (2008, methodology): “X = fXtgt2R is a strictly stationary fiiFr· echet process called mixed moving maxima (see Stoev and Taqqu (2005) ).”