Well-posedness of Backward Stochastic Differential Equations with General Filtration

摘要

This paper is addressed to the well-posedness of some linear and semilinearbackward stochastic differential equations with general filtration, withoutusing the Martingale Representation Theorem. The point of our approach is tointroduce a new notion of solution, i.e., the transposition solution, whichcoincides with the usual strong solution when the filtration is natural but itis more flexible for the general filtration than the existing notion ofsolutions. A comparison theorem for transposition solutions is also presented.