The primary concern of this paper is to calculate the distributions and/or means of the maxima, first entrance times, and occupation times of Brownian meander and Brownian excursion. The method employed is to develop conditioned families of random functions which have Brownian meander (or Brownian excursion) as their weak limit and then use the continuous mapping theorem.
"Functionals of Brownian Meander and Brownian Excursion." Ann. Probab. 5 (1) 130 - 135, February, 1977. https://doi.org/10.1214/aop/1176995896