Continuous dependence property of BSDE with constraints

Abstract: In this paper, we study continuous properties of adapted solutions for backward stochastic differential equations with constraints (CBSDEs in short). Comparing with many existing literatures about this topic, our case is very general in the sense that constraints are formulated by general non-negative real functions. In general case, we proved a continuous property from below and a lower semi-continuous property of the minimal super-solution of CBSDE in its effective domain. Furthermore, in the special convex case, we obtained a continuous property with the help of convex analysis.