The equivalence between uniqueness and continuous dependence of solutions for FBSDEs with continuous monotone coefficients

In this paper we study one kind of coupled forward–backward stochastic differential equation. With some particular choice for the coefficients, if one of them satisfies a uniform growth condition and they are accordingly monotone, then we obtain the equivalence between the uniqueness of solution and its continuous dependence on x and ξ , where x is the initial value of the forward component and ξ is the terminal value of the backward component.