The continuous and discrete Brownian bridges: Representations and applications
The authors give a brief exposition of (discrete) Brownian motion and Brownian bridge processes. In particular, they establish spectral representations of the (discrete) processes in terms of (finite) sums of weighted and independent standard normal random variables. Applications to goodness-of-fit testing for uniform distributions, discrete uniform distributions, uniform distributions with censored data, and locally invariant tests are given. In the last section, it is suggested how discrete representations could be used in simulation studies.
scientific article; zbMATH DE number 1076287