Perfect simulation of spatial processes. 23rd Brazilian mathematics colloquium, Rio de Janeiro, Brazil, July 23--27, 2001 (Q2753395)

The paper is devoted to the simulation from invariant distributions of spatial birth and death processes. In contrast to the classical Markov chain Monte Carlo approach at which the invariant measure is approximated by a distribution of the chain after long run, the author concentrates on the simulation perfectly from the invariant distribution. General theory of spatial birth and death processes is developed in the second chapter. It includes the construction of the processes, description of invariant measures and ergodicity theory. Point processes which can be obtained as invariant distributions of birth and death processes are described in the first chapter (e.g. Strauss processes, Ising models, loss networks). In the third chapter main algorithms of perfect simulation are considered, such as Propp and Wilson's coupling from the past algorithm, Fill's interruptible algorithm and backward-forward algorithm. The problem of user impatience bias is discussed. Applications to attractive spin systems and ferromagnetic Ising model are described.