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.
