The authors study the continuous properties of square integrable g-martingales via backward stochastic differential equations (shortly BSDEs) and get a general upcrossing inequality and an optional stopping theorem fo...The authors study the continuous properties of square integrable g-martingales via backward stochastic differential equations (shortly BSDEs) and get a general upcrossing inequality and an optional stopping theorem for g-martingales.展开更多
A maximum principle is proved for semilinear stochastic evolution systems. The main contribution of this work is that in our problem, the infinitesimal generator of the semigroup of the systems need not to be elliptic...A maximum principle is proved for semilinear stochastic evolution systems. The main contribution of this work is that in our problem, the infinitesimal generator of the semigroup of the systems need not to be elliptic. This generalizes a result of A. Bensoussan in 1983.展开更多
For a nonlinear equation, a global representation for all solutions is obtained. Via this represention, a nonlinear generalized inverse theorem is derived and an application to control systems with mixture constraints...For a nonlinear equation, a global representation for all solutions is obtained. Via this represention, a nonlinear generalized inverse theorem is derived and an application to control systems with mixture constraints is given as well.展开更多
基金Project supported by the National Natural Science Foundation of China (No.79790130).
文摘The authors study the continuous properties of square integrable g-martingales via backward stochastic differential equations (shortly BSDEs) and get a general upcrossing inequality and an optional stopping theorem for g-martingales.
基金Partially supported by Chinase National Science Foundation
文摘A maximum principle is proved for semilinear stochastic evolution systems. The main contribution of this work is that in our problem, the infinitesimal generator of the semigroup of the systems need not to be elliptic. This generalizes a result of A. Bensoussan in 1983.
基金Projects supported in part by the Chinese National Natural Science Fundation under Grant 01884 16
文摘For a nonlinear equation, a global representation for all solutions is obtained. Via this represention, a nonlinear generalized inverse theorem is derived and an application to control systems with mixture constraints is given as well.
