Some new classes of stationary max-stable random fields

We present two new classes of stationary max-stable random fields. For the first class, we use the spectral representation due to Schlather (2002) and assume that the stationary process used in the representation is proportional to a power of a max-stable random field. We derive the finite dimensional distributions, explain the relationship between distributions of both max-stable random fields and give sufficient conditions for the sample paths to be γ-Hölder continuous functions for some γ∈(0,1). For the second class, we consider a multiplicative factor model and a Poisson–Voronoï tessellation of Rd to construct new max-stable random fields. We provide explicit expressions for the pairwise distribution function.