  In this paper we study an Ergodic Markovian BSDE involving a forward process
$X$ that solves an infinite dimensional forward stochastic evolution equation
with multiplicative and possibly degenerate diffusion coefficient. A concavity
assumption on the driver allows us to avoid the typical quantitative conditions
relating the dissipativity of the forward equation and the Lipschitz constant
of the driver. Although the degeneracy of the noise has to be of a suitable
type we can give a stochastic representation of a large class of Ergodic HJB
equations; morever our general results can be applied to get the synthesis of
the optimal feedback law in relevant examples of ergodic control problems for
SPDEs.
