On the distribution of a max-stable process conditional on max-linear functionals

Recently, Dombry and Éyi-Minko (2013) provided formulae for the distribution of a max-stable process conditional on its values at given sites and proposed a methodology for sampling from this distribution. We generalize their results by allowing for conditions stemming from max-linear functionals of the process. Furthermore, we show that the conditional distribution of the extremal functions, i.e. the spectral functions attaining the imposed conditions, is closely related to the normalized spectral representation. The results are illustrated in several examples.