In this paper we study ergodic backward stochastic differential equations
(EBSDEs) dropping the strong dissipativity assumption needed in the previous
work. In other words we do not need to require the uniform exponential decay of
the difference of two solutions of the underlying forward equation, which, on
the contrary, is assumed to be non degenerate. We show existence of solutions
by use of coupling estimates for a non-degenerate forward stochastic
differential equations with bounded measurable non-linearity. Moreover we prove
uniqueness of "Markovian" solutions exploiting the recurrence of the same class
of forward equations. Applications are then given to the optimal ergodic
control of stochastic partial differential equations and to the associated
ergodic Hamilton-Jacobi-Bellman equations
