Stationarity of multivariate particle systems
  A particle system is a family of i.i.d. stochastic processes with values translated by Poisson points. We obtain conditions that ensure the stationarity in time of the particle system in R^d and in some cases provide a full characterisation of the stationarity property. In particular, a full characterisation of stationary multivariate Brown-Resnick processes is given. 
Ilya Molchanov and Kaspar Stucki
math.PR