  The "weighted ensemble" method, introduced by Huber and Kim, [G. A. Huber and
S. Kim, Biophys. J. 70, 97 (1996)], is one of a handful of rigorous approaches
to path sampling of rare events. Expanding earlier discussions, we show that
the technique is statistically exact for a wide class of Markovian and
non-Markovian dynamics. The derivation is based on standard path-integral (path
probability) ideas, but recasts the weighted-ensemble approach as simple
"resampling" in path space. Similar reasoning indicates that arbitrary
nonstatic binning procedures, which merely guide the resampling process, are
also valid. Numerical examples confirm the claims, including the use of bins
which can adaptively find the target state in a simple model.
