Functionals of Brownian Meander and Brownian Excursion.

摘要

Brownian meander and Brownian excursion processes arise as the limit process of a number of conditional functional central limit theorems. To reap the full benefit of such limit theorems one needs to know the distribution of functionals of the limit process. In this paper the distribution of the maxima, first entrance times, and expected occupation time densities are computed for the two limit processes. This is done by using the methods of weak convergence.