Mathematical Sciences: Markov Processes

该项目的一般研究领域是马尔可夫过程的游程和局部时，例如布朗运动。作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关于布朗运动的积分的许多重要问题。新泛函是布朗运动函数的积分。这类泛函的例子包括扇区的占用时间和布朗词。最后是对该过程的自动缠绕行为的衡量。在本地时间观察的本地时间过程导致更一般的过程的存在性问题。其中一些问题是由克莱因的弦理论解决的。由布朗运动的最后一次极小过程产生的反正弦过程具有许多有趣的性质，但至今仍未被研究。

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.