  We provide an algorithm based on weighted-ensemble (WE) methods, to
accurately sample systems at steady state. Applying our method to different
one- and two-dimensional models, we succeed to calculate steady state
probabilities of order $10^{-300}$ and reproduce Arrhenius law for rates of
order $10^{-280}$. Special attention is payed to the simulation of
non-potential systems where no detailed balance assumption exists. For this
large class of stochastic systems, the stationary probability distribution
density is often unknown and cannot be used as preknowledge during the
simulation. We compare the algorithms efficiency with standard Brownian
dynamics simulations and other WE methods.
