Nonlinear decomposition of Doob-Meyer’s type for continuous \(g\)-supermartingale with uniformly continuous coefficient. (English) Zbl 1406.60065

Shi, Xuejun; Jiang, Long; Ji, Ronglin

J. Appl. Math. 2014, Article ID 743508, 9 p. (2014).

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.

MSC:

60G48	Generalizations of martingales
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)