Well-posedness of Backward Stochastic Differential Equations with General Filtration

Details Well-posedness of Backward Stochastic Differential Equations with General Filtration Well-posedness of Backward Stochastic Differential Equations with General Filtration

2010-09-30

arxiv.org/abs/1010.0026v3

Mathematics

Probability

21 pages

Scientific paper

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.

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