The Equivalence between Uniqueness and Continuous Dependence of Solution   for BSDEs with Continuous Coefficient
  In this paper, we will prove that, if the coefficient $g=g(t,y,z)$ of a BSDE is assumed to be continuous and linear growth in $(y,z)$, then the uniqueness of solution and continuous dependence with respect to $g$ and the terminal value $\xi$ are equivalent. 
Guangyan Jia, Zhiyong Yu