Brownian bridge

Summary

A Brownian bridge is a Brownian motion on $[0, 1]$ forced to return to $0$ at time $1$. It is a continuous centred Gaussian process with covariance $\min(s, t) - st$. It is the limit of the uniform empirical process, which makes it central in goodness-of-fit tests such as the Kolmogorov–Smirnov test.