  This paper is addressed to the well-posedness of some linear and semilinear
backward stochastic differential equations with general filtration, without
using the Martingale Representation Theorem. The point of our approach is to
introduce a new notion of solution, i.e., the transposition solution, which
coincides with the usual strong solution when the filtration is natural but it
is more flexible for the general filtration than the existing notion of
solutions. A comparison theorem for transposition solutions is also presented.
