Mathematical Sciences: Research on Stochastic Process and Large Deviation Theory

首席研究员将在随机过程理论的三个领域进行研究。 有两个领域与大偏差理论有关。 第一个涉及用“不连续统计”证明马尔可夫随机过程的基本大偏差原理，这一类包括具有不连续漂移和小扩散系数的扩散以及某些缩放的排队系统。 第二个领域涉及数值和模拟方法。 第三个研究领域涉及发展 Skorokhod 问题解决方案的理论和应用，这是研究各种“约束”随机过程的基本且有用的工具。 首席研究员将研究随机（随机）过程理论的几个领域。 其中一个领域涉及用“不连续统计”证明马尔可夫随机过程的基本大偏差原理。 这类随机过程在随机控制的某些应用中很重要。

The principal investigator will conduct research in three areas of the theory of stochastic processes. Two areas have to do with large deviation theory. The first concerns proving the fundamental large deviation principle for Markov stochastic processes with "discontinuous statistics", a class that includes diffusions with discontinuous drift and small diffusion coefficient as well as certain scaled queueing systems. The second area involves numerical and simulation methods. The third area of study is concerned with developing the theory and applications of the solution to the Skorokhod Problem, which is a basic and useful tool in the study of various "constrained" stochastic processes. The principal investigator will study several areas of the theory of stochastic (random) processes. One of the areas involves proving the fundamental large deviation principle for Markov stochastic processes with "discontinuous statistics". This class of stochastic processes is important in certain applications of stochastic control.