  As an example for the fast calculation of distributional parameters of
Gaussian processes, we propose a new Monte Carlo algorithm for the computation
of quantiles of the supremum norm of weighted Brownian bridges. As it is known,
the corresponding distributions arise asymptotically for weighted CUSUM
statistics for change-point detection. The new algorithm employs an adaptive
(sequential) time discretization for the trajectories of the Brownian bridge. A
simulation study shows that the new algorithm by far outperforms the standard
approach, which employs a uniform time discretization.
