LIMIT THEOREMS FOR BACKWARD STOCHASTIC EQUATIONS

SERGEY YA. MAKHNO AND IRINA A. YERISOVA
Theory of Stochastic Processes Vol. 14 (30), no. 2, 2008, pp. 93–107
Consider a weak convergence in Meyer-Zheng topology of solutions of backward stochastic equation in form
$$
Y^\epsilon(t)=E\biggl[g^\epsilon\biggl(X^\epsilon(T)\biggl)+\int^T_t
f^\epsilon\biggl(s,X^\epsilon(s),Y^\epsilon(s)\biggl)ds\biggl\vert%\Cal
F^{X^\epsilon}_t\biggl]
$$
as $\epsilon\to 0$ for different classes of random processes $X^\epsilon(t)$ with irregularly dependence on parameter $\epsilon$. The equations for limit process are obtained.
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