Stationary min-stable stochastic processes

Summary We consider the class of stationary stochastic processes whose margins are jointly min-stable. We show how the scalar elements can be generated by a single realization of a standard homogeneous Poisson process on the upper half-strip 0,1]×R ₊ and a group of L ₁-isometries. We include a Dobrushin-like result for the realizations in continuous time.