Weak existence and uniqueness for forward-backward SDEs (Q860697)

Under certain conditions, weak existence and uniqueness is proved for solutions of the forward-backward system of stochastic differential equations \[ X_s= x+ \int^s_t b(r, X_r, Y_r, Z_r)\,dr+ \int^s_t \sigma(r, X_r, Y_r)\,dB_r, \] \[ Y_s= G(X_T)+ \int^T_s f(r, X_r, Y_r, Z_r)\,dr- \int^T_s\langle Z_r, \sigma(r, X_r, Y_r)\,dB_r\rangle, \] where \(s\in[t, T]\) and \(f\) is allowed to grow quadratically in \(Z\).