Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type

We have obtained the following limit theorem: if a sequence of RCLL superso lutions of a backward stochastic differential equations (BSDE) converges mo notonically up to (y(t)) with E[sup(t) \y(t)\(2)] < infinity, then (y(t)) i tself is a RCLL supersolution of the same BSDE (Theorem 2.4 and 3.6). We apply this result to the following two problems: 1) nonlinear Doob-Meyer Decomposition Theorem. 2) the smallest supersolution of a BSDE with constr aints on the solution (y, z). The constraints may be non convex with respec t to (y, z) and may be only measurable with respect to the time variable t. this result may be applied to the pricing of hedging contingent claims wit h constrained portfolios and/or wealth processes.