Spatial Stochastic Framework for Sampling Time Parametric Max-stable Processes

Abstract

Modelling the spatial extreme events uses the approach of max-stable processes which describe the stochastic behaviour of point-referenced data. Max-stable processes form the natural extension of multivariate extreme values distributions to infinite dimensions. In this paper we consider a max-stable stochastic process over space index. We extend the modelling to time-varying setting using new characterizations of the multivariate distribution underlying the process. A distortional measure is introduced to describe the marginal laws and joint dependence.