Nonequilibrium fluctuations in particle systems modelling reaction-diffusion equations

We consider a class of stochastic evolution models for particles diffusing on a lattice and interacting by creation-annihilation processes. The particle number at each site is unbounded. We prove that in the macroscopic (continuum) limit the particle density satisfies a reaction-diffusion PDE, and that microscopic fluctuations around the average are described by a generalized Ornstein-Uhlenbeck process, for which the covariance kernel is explicitely exhibited.