  We propose a novel stochastic method to exactly generate Brownian paths
conditioned to start at an initial point and end at a given final point during
a fixed time $t_{f}$. These paths are weighted with a probability given by the
overdamped Langevin dynamics. We show how these paths can be exactly generated
by a local stochastic differential equation. The method is illustrated on the
generation of Brownian bridges, Brownian meanders, Brownian excursions and
constrained Ornstein-Uehlenbeck processes. In addition, we show how to solve
this equation in the case of a general force acting on the particle. As an
example, we show how to generate constrained path joining the two minima of a
double-well. Our method allows to generate statistically independent paths, and
is computationally very efficient.
