  We propose a novel stochastic method to generate paths conditioned to start
in an initial state and end in a given final state during a certain time
$t_{f}$. These paths are weighted with a probability given by the overdamped
Langevin dynamics. We show that these paths can be exactly generated by a
non-local stochastic differential equation. In the limit of short times, we
show that this complicated non-solvable equation can be simplified into an
approximate stochastic differential equation. For longer times, the paths
generated by this approximate equation can be reweighted to generate the
correct statistics. In all cases, the paths generated by this equation are
statistically independent and provide a representative sample of transition
paths. In case the reaction takes place in a solvent (e.g. protein folding in
water), the explicit solvent can be treated. The method is illustrated on the
one-dimensional quartic oscillator.
