Backward Stochastic Evolution Equations

In this chapter, we present an introduction to backward stochastic evolution equations (valued in Hilbert spaces), which appear naturally in the study of control problems for stochastic distributed parameter systems. In the case of natural filtration, by means of the Martingale Representation Theorem, these equations are proved to be well-posed in the sense of mild solutions; while for the general filtration, using our stochastic transposition method, we also establish their well-posedness.