雍炯敏教授系列报告 (IV-VI) 与研讨班
系列报告题目: Deterministic and Stochastic Dynamic Equations
系列报告时间: 2018年07月19日, 20日, 23日下午3:30-5:30
系列报告地点: 数学楼 145 报告厅或 144 教室
Part I. A Deterministic Theory.
We recall ordinary differential equations (ODEs, for short), including well-posedness theorem and comparison theorem of initial value problems, terminal value problems. For two-point boundary value problems, inspired by the invariant imbedding, we will obtain representation theorem for the backward component via a solution to a partial differential equation (PDE) together with the forward component. Also, we will look at the corresponding results for forward Volterra integral equations (FVIEs) and backward Volterra integral equations (BVIEs). It turns out that some extensions of the results for ODEs to VIEs are not trivial.
Part II. Forward Stochastic Differential Equations and Backward Stochastic Differential Equations.
We recall some standard theory for (forward) stochastic differential equations (FSDEs). Then a brief theory for backward stochastic differential equations (BSDEs) will be presented, including well-posedness and comparison theorem. Feynman-Kac formula and representation theorem will be presented. For (coupled) forward-backward stochastic differential equations (FBSDEs), some standard methods will be surveyed for the solvability.
Part III. Forward Stochastic Volterra Integral Equations and Backward Stochastic Volterra Integral Equations.
We will try to extend the theory for FSDEa and BSDEs to forward stochastic Volterra integral equations (FSVIEs) and backward stochastic Volterra integral equations (BSVIEs). The extension will involve quite a lot, and some of them are still at the stage of ongoing research projects.
研讨班参与人: 雍炯敏教授, 向淑晃教授, 杨东辉教授, 周越 (博士生), 黄建平 (博士生), 以及若干硕士生与本科生
研讨班时间: 2018年07月19日至2018年07月27日上午 8:30-11:30
研讨班地点: 数学院 144教室