Conditional simulation of max-stable processes

Since many environmental processes are spatial in extent, a single extreme event may affect several locations, and the spatial dependence must be taken into account in an appropriate way. This paper proposes a framework for conditional simulation of max-stable processes and gives closed forms for the regular conditional distributions of Brown-Resnick and Schlather processes. We test the method on simulated data and present applications to extreme rainfall around Zurich and extreme temperatures in Switzerland. The proposed framework provides accurate conditional simulations and can handle problems of realistic size.