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

Abstract

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.