Mathematical Sciences: Research on Optimal Stochastic Control and Nonlinear Estimation

这项研究是正在进行的计划的一部分， 首席调查员和同事 以下主题 研究的领域有：（1）受控马尔可夫扩散 和非线性偏微分方程;（2）渐近性质的近 确定性马尔可夫过程;（3）金融经济学 应用;（4）奇异随机控制;（5）计算 随机控制方法;（6）随机微积分 （7）非线性估计。 分析方法基于 关于非线性微分方程的粘性解法 方程以及概率方法将被研究。 这些理论研究是应用问题的基础 从股票市场层面的决策到 宇宙飞船

This research is part of an on-going program by the principal investigator and associates. Topics in the following areas are to be considered: (1) controlled Markov diffusions and nonlinear PDEs; (2) asymptotic properties of nearly deterministic Markov processes; (3) financial economics applications; (4) singular stochastic control; (5) computational methods in stochastic control; (6) stochastic calculus of variations; (7) nonlinear estimation. Analytical methods based on viscosity solution techniques for nonlinear differential equations as well as probabilistic methods will be studied. These theoretical studies are the basis for applied problems ranging from decisions at the stock market level to the control of spaceships.