Mathematical Sciences: Stochastic Analysis and Geometry

随机几何和随机Lyapunov稳定性理论中的并行程序的研究将继续下去。在前一个方向，研究将涉及各向同性传输过程的递归和本征函数展开的项目，两者都是在黎曼流形的背景下进行的。关于Lyapunov稳定性的工作将研究带边界条件的非线性振动和波动方程。还继续为中西部概率讨论会提供支助，该讨论会现在是概率论领域的一项重要年度活动。概率论中的数学研究在自然科学和社会科学中都被用作建模的工具。该奖项将继续开发这些工具。此外，它还将为一次会议提供支持，该会议非常成功地将来自许多专业领域的研究人员聚集在一起。

Research will continue on parallel programs in stochastic geometry and stochastic Lyapunov stability theory. In the former direction research will involve the recurrence of isotropic transport processes and a project on eigenfunction expansions, both in the context of Riemannian manifolds. The work on Lyapunov stability will investigate nonlinear oscillations and wave equations with boundary conditions. Continued support is also being provided for the Midwest Probability Colloquium, which now functions as a major annual event in the field of probability theory. Mathematical research in probability theory is used as a tool for modeling in both the physical and social sciences. This award will continue the development of these tools. In addition it will provide support for a meeting which has been very successful in bringing together research workers from many specialty areas.