Eva Löcherbach

I will present a (partly) new method for perfectly sampling from the stationary regime of point processes having an infinite number of interacting components. This method is based on what is called Kalikow decomposition of the stochastic intensity of the process, together with an exploration of the spatial-temporal past of the process called Clan-of-Ancestors method. Such decompositions have been introduced in the framework of discrete time processes with long memory and/or g-measures, by Kalikow in 1990. I will explain how this method can be generalized to the framework of point processes in continuous time and which are the limitations of this approach. Finally I will discuss several examples, in particular Hawkes processes with an infinite number of components, having a strict refractory period. My talk is based on joint work with Patricia Reynaud-Bouret and Tien Cuong Phi (Nice).