Mathematical Sciences: Research in Stochastic Process Theory

首席研究员将在随机过程理论和相关偏微分方程的三个领域进行研究。第一个领域是关于证明具有“不连续统计”的马尔可夫随机过程的大偏差原理，这类过程包括具有不连续漂移和小扩散系数的扩散以及某些缩放排队系统。第二部分研究了一类重要跳跃马尔可夫过程的完全渐近展开问题。本文的最后一部分工作涉及连续时间随机控制问题的数值方法研究。首席研究员将对随机过程（概率论的一个分支）和随机控制（应用数学的一个分支）之间的几个问题进行研究。这些问题是由理解队列系统所涉及的问题引起的，这在许多应用程序中都会自然出现，例如通信。

The principal investigator will conduct research in three areas of the theory of stochastic processes and related partial differential equations. The first area is concerned with proving the 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 considers the problem of obtaining the full asymptotic expansion for certain important classes of jump Markov processes. The last part of the proposed work involves research in the area of numerical methods for continuous time stochastic control problems. The principal investigator will conduct research on several problems that are at the interface of stochastic processes, a branch of probability theory, and stochastic control, a branch of applied mathematics. The problems are motivated by issues involved with understanding systems of queues, which arise naturally in several applications, for example communications.