We prove that a continuous -supermartingale with uniformly continuous coeffcient on finite or infinite horizon, is a -supersolution of the corresponding backward stochastic differential equation. It is a new nonlinear Doob-Meyer decomposition theorem for the -supermartingale with continuous trajectory.
"Nonlinear Decomposition of Doob-Meyer's Type for Continuous -Supermartingale with Uniformly Continuous Coefficient." J. Appl. Math. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/743508