  A new Monte-Carlo method for solving linear parabolic partial differential
equations is presented. Since, in this new scheme, the particles are followed
backward in time, it provides great flexibility in choosing critical points in
phase-space at which to concentrate the launching of particles and thereby
minimizing the statistical noise of the sought solution. The trajectory of a
particle, Xi(t), is given by the numerical solution to the stochastic
differential equation naturally associated with the parabolic equation. The
weight of a particle is given by the initial condition of the parabolic
equation at the point Xi(0). Another unique advantage of this new Monte-Carlo
method is that it produces a smooth solution, i.e. without delta-functions, by
summing up the weights according to the Feynman-Kac formula.
