Mathematical Sciences: Partial Differential Equations and Probability

该项目将考虑解决方案的规律性， 退化椭圆方程，受控扩散过程， 和伊藤的随机方程 各种技术， 将利用偏微分方程和概率。 这些包括障碍，边界算子的研究， 拟导数 该项目的结果，除了进一步促进我们的 理解偏微分方程解的性质 方程，将应用于金融等领域， 种群遗传学和化学系统的控制。

This project will consider regularity of solutions to degenerate elliptic equations, controlled diffusion processes, and Ito's stochastic equations. A variety of techniques from partial differential equations and probability will be utilized. These include barriers, study of boundary operators, and quasiderivatives. The results of this project, in addition to furthering our understanding of the nature of solutions to partial differential equations, will have applications to areas such as finance, population genetics, and control of chemical systems.