Under the Lipschitz assumption and square integrable assumption on g, Jiang proved that Jensen＇s inequality for BSDEs with generator g holds in general if and only if g is independent of y, g is super homogenous in z...Under the Lipschitz assumption and square integrable assumption on g, Jiang proved that Jensen＇s inequality for BSDEs with generator g holds in general if and only if g is independent of y, g is super homogenous in z and g（t, 0） = 0, a.s., a.e.. In this paper, based on Jiang＇s results, under the same assumptions as Jiang＇s, we investigate the necessary and sufficient condition on g under which Jensen＇s inequality for BSDEs with generator g holds for some specific convex functions, which generalizes some known results on Jensen＇s inequality for BSDEs.展开更多
In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen＇s inequality. Some new stability theorems are obtained. Examples are given...In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen＇s inequality. Some new stability theorems are obtained. Examples are given to demonstrate the advantage of the obtained results.展开更多
基金Supported by National Natural Science Foundation of China (Grant No.10671205)Youth Foundation of CUMT (Grant Nos.2006A041 and 2007A029)
文摘Under the Lipschitz assumption and square integrable assumption on g, Jiang proved that Jensen＇s inequality for BSDEs with generator g holds in general if and only if g is independent of y, g is super homogenous in z and g（t, 0） = 0, a.s., a.e.. In this paper, based on Jiang＇s results, under the same assumptions as Jiang＇s, we investigate the necessary and sufficient condition on g under which Jensen＇s inequality for BSDEs with generator g holds for some specific convex functions, which generalizes some known results on Jensen＇s inequality for BSDEs.
基金supported by the National Natural Science Foundation of China (No. 10871063)Scientific Research Fund of Hunan Provincial Education Department (No. 07A038)
文摘In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen＇s inequality. Some new stability theorems are obtained. Examples are given to demonstrate the advantage of the obtained results.
