Ergodic BSDEs and related PDEs with Neumann boundary conditions under weak dissipative assumptions

Abstract: 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 $\R^d$ not necessary bounded. We study the link of such EBSDEs with PDEs and we apply our results to an ergodic optimal control problem.