Theoretical and numerical study of stochastic backward differential equations.

Summary In a first step, we study a new class of backward stochastic differential equations (denoted EDSRs) which are related to semi-linear Neumann conditions for ergodic phenomena. The particularity of these problems is that the ergodic constant appears in the edge condition. We study the existence and uniqueness of solutions for such ergodic EDSRs as well as the link with partial differential equations and we apply these results to optimal ergodic control problems. In a second part we generalize the work of P.