Limit theorems for backward stochastic equations

Consider a weak convergence in the Meyer–Zheng topology of solutions of a backward stochastic equation in the form
$$ Y^\epsilon(t)=E\Big[g^\epsilon(X^\epsilon(T))+\int^T_tf^\epsilon(s, X^\epsilon(s), Y^\epsilon(s)ds\Big|F_t^{X^\epsilon})\Big] $$
as $\epsilon>0$ for different classes of random processes $X^\epsilon(t)$ with the irregular dependence on the parameter $\epsilon.$ The equations for the limit process are obtained.