Nonlinear decomposition of Doob-Meyer's type for continuous \(g\)-supermartingale with uniformly continuous coefficient (Q1714741)

Summary: 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.