I am trying to find a theorem which my old teacher showed me a long time ago. The implication of this theorem was that if we had a random sample $X_1,X_2,...,X_n$ and we consider the process:
$$B(t) = \sqrt n \sum_{i=1}^t (X_i-\bar{X_n})$$
Is asymptotically a Brownian bridge. The process above was defined using $nt$ instead of just $t$, but I can't recall how... The purpose of this theorem was to construct a Brownian bridge so that we can apply the kolmogorov-smirnov test in order to detect a change in mean.
I've tried google searches but it just leads me to generic papers on brownian bridge and brownian motion.