Mathematical Sciences: Markov Processes

该项目的一般研究领域是马尔可夫过程（如布朗运动）的短途和局部时间。研究者将继续研究布朗运动的加性泛函的渐近性质。之前与你合作的工作，解决了许多关于布朗运动积分的重要问题。新的泛函是布朗运动函数的积分。这类函数的例子包括扇区的占用时间和布朗词。最后是对过程的自缠绕行为的度量。在当地时间观察的当地时间过程导致了更一般过程的存在性问题。克莱恩的弦理论解决了其中的一些问题。由布朗运动最后一次极小值过程产生的反正弦过程有许多有趣的性质，迄今尚未被探索。

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.