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 supersolutions of a backward stochastic differential equations (BSDE) converges monotonically up to (y(t)) with E[sup(t) \y(t)\(2)] < infinity, then (y(t)) itself 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 constraints on the solution (y, z). The constraints may be non convex with respect 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 with constrained portfolios and/or wealth processes.