Mathematical Sciences: Markov Processes

本项目的一般调查范围是 马尔可夫过程的局部时间和局部时间，例如 布朗运动 研究者将继续研究 布朗运动可加泛函的渐近性质 以前与Yor合作的工作，已经解决了许多 关于积分的重要问题 布朗运动 新的泛函是函数的积分 布朗运动。 这样的泛函的示例包括 扇区的占据时间和布朗词。 最后是一个 测量过程的自缠绕行为。 当地 从局部时间看时间过程，存在性问题 更一般的过程。 其中一些问题得到了解决 克莱因的弦理论 一个反正弦过程， 布朗运动的最后一次极小过程有许多 有趣的特性，尚未被探索。

The general area of investigation in the project is excursions and local times of Markov processes such as the Brownian motion. The investigator will continue the study of asymptotic properties of additive functionals of Brownian motion. Previous work in collaboration with Yor, has settled many important questions about the integrals with respect to the Brownian motion. The new functionals are integrals of functions of Brownian motion. Examples of such functionals include the occupation times of sectors and Brownian Words. The last is a measure of the self winding behavior of the process. The local time process viewed at local times leads to existence questions of more general processes. Some of these questions are settled by Krein's theory of strings. An arcsin process arising from the process of the last time minimum of Brownian motion has many interesting properties and has been as yet, unexplored.