Nonlinear Decomposition of Doob-Meyer's Type for Continuous g-Supermartingale with Uniformly Continuous Coefficient

We prove that a continuous g-supermartingale with uniformly continuous coeffcient g on finite or infinite horizon, is a g-supersolution of the corresponding backward stochastic differential equation. It is a new nonlinear Doob-Meyer decomposition theorem for the g-supermartingale with continuous trajectory