The behavior of multivariate maxima of moving maxima processes

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Conditional sampling for spectrally discrete max-stable random fields (2010, methodology): “to represent well the complex spatial dependence structure in the data. On the other hand, the conditional sampling methodology applies to arbitrary discrete max-linear models. Following the ideas of [31], one could obtain very ﬂexible models by combining independent maxima of moving maxima. Namely,”
Extremal stochastic integrals: a parallel between max-stable processes and α-stable processes (2005, methodology): “Statistical properties of the M4 of processes were also studied by Zhang and Smith (2004).”
On the estimation and application of max-stable processes (2010, background): “We have a general joint probability formula (Zhang and Smith, 2004): where a l,k,d = 0 when the triple subindex is outside the range defined in (2.1).”
Stationary max-stable fields associated to negative definite functions. (2008, methodology): “First, we recall a definition of mixed moving maxima processes as given in [27, 30]; see also [14, 29, 31].”
Regularly varying multivariate time series (2007, background): “, 2002b), and moving maxima processes with heavy-tailed innovations (Davis and Resnick, 1989, 1993; Zhang and Smith, 2004).”