Well-posedness of Backward Stochastic Differential Equations with General Filtration

2010/09/30 by Qi Lü, Xu Zhang, Lu, Qi +1
Computer Science · Economics, Econometrics and Finance · Engineering · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1010.0026

openalex publication_date 2010/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Exact Controllability, Stabilization and Perturbations for Distributed Systems
• Representation of Itô Integrals by Lebesgue/Bochner Integrals

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