Weak Solutions of Forward-Backward SDEs and Their Uniqueness
نویسندگان
چکیده
In this paper we propose a new notion of Forward-Backward Martingale Problem (FBMP), and study its relationship with the weak solution to the backward stochastic differential equations. The FBMP extends the idea of the well-known (forward) martingale problem of Stroock and Varadhan, but it is structured specifically to fit the nature of a forward-backward stochastic differential equation (FBSDE). Assuming that the FBSDE is Markovian with Hölder continuous coefficients we show that the solution to the FBMP does exist. Furthermore, we prove that the uniqueness of the FBMP (whence the uniqueness of the weak solution) is determined by the uniqueness of the viscosity solution of the corresponding quasilinear PDE.
منابع مشابه
Weak Solutions for Forward – Backward Sdes — a Martingale Problem Approach
In this paper, we propose a new notion of Forward–Backward Martingale Problem (FBMP), and study its relationship with the weak solution to the forward–backward stochastic differential equations (FBSDEs). The FBMP extends the idea of the well-known (forward) martingale problem of Stroock and Varadhan, but it is structured specifically to fit the nature of an FBSDE. We first prove a general suffi...
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