Equivalence of ensembles in creation-annihilation nonequilibrium models

We consider a class of stochastic models on a lattice in which particles are created and annihilated with given rates. The class include very distinct models such as the contact process and the stochastic Ising model. We show how to set up stochastic models with the dynamics that conserve the number of particles that are equivalent, in the thermodynamic limit, to the creation-annihilation models. We also obtain a formula that allows the calculation of the rates with respect to the ensemble of constant particle number.