Multivariate max-stable processes are important for both theoretical investigations and various statistical applications motivated by the fact that these limiting processes, instance of stationary multivariate regularly varying time series, (Dombry et al., 2018). In this contribution we explore relation between homogeneous functionals discuss connections process zonoid/max-zonoid equivalence. W...

The multivariate extremal index has been introduced by Nandagopalan as a measure of the clustering among the extreme values of a multivariate stationary process. In this paper, we derive some additional properties and use those to construct a statistical estimation scheme. Central to the discussion is a class of processes we call M 4 processes, which are characterized by means of a multivariate...

Abstract. We give a simple method to approximate multidimensional exponentially tempered stable processes and show that the approximating process converges in the Skorokhod topology to the tempered process. The approximation is based on the generation of a random angle and a random variable with a lower dimensional Lévy measure. We then show that if an arbitrarily small normal random variable i...