We study a class of ergodic BSDEs related to PDEs with Neumann boundary
conditions. The randomness of the drift is given by a forward process under
weakly dissipative assumptions with an invertible and bounded diffusion matrix.
Furthermore, this forward process is reflected in a convex subset of Rd not
necessary bounded. We study the link of such EBSDEs with PDEs and we apply our
results to an ergodic optimal control problem