Perfect simulation using dominating processes on ordered spaces, with application to locally stable point processes

In this paper we investigate the application of perfect simulation, in part icular Coupling from the Past (CFTP), to the simulation of random point pro cesses. We give a general formulation of the method of dominated CFTP and a pply it to the problem of perfect simulation of general locally stable poin t processes as equilibrium distributions of spatial birth-and-death process es. We then investigate discrete-time Metropolis-Hastings samplers for poin t processes, and show how a variant which samples systematically from cells can be converted into a perfect version. An application is given to the St rauss point process.