Grant number: 05/00248-6 Support Opportunities: Scholarships in Brazil - Post-Doctorate Effective date (Start): November 01, 2005 Effective date (End): February 28, 2007 Field of knowledge: Physical Sciences and Mathematics - Mathematics Principal Investigator: Nancy Lopes Garcia Grantee: Marcelo Ventura Freire Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil Abstract Perfect simulation methods have been applied successfully to Markovian processes, such as the one-dimensional, continuous, unbounded loss network. The construction of he perfect simulation is granted if the loss network is dominated by a subcritical percolation process, which can be dominated by a branching process.It was proved that a second order construction of the branching process improves the estimate of the critical rate $\lambda_c$ that ensures the construcution. We will build greater order braching processes as approximations of an infinite order process to get the rate $\lambda_c$ at the limit.As an application, we will use these results to build a perfect simulation scheme for the RJMCMC, which is employed to simulate posteriori distributions of variable dimension models.