Multivariate max-stable spatial processes

Max-stable processes allow the spatial dependence of extremes to be modelled and quantified, so they are widely adopted in applications. For a better understanding of extremes, it may be useful to study several variables simultaneously. To this end, we study the maxima of independent replicates of multivariate processes, both in the Gaussian and Student-t cases. cases. We define a Poisson process construction and introduce multivariate versions of the Smith Gaussian extreme-value, the Schlather extremal-Gaussian and extremal-t, and the Brown–Resnick models.