A new Monte-Carlo method for solving linear parabolic partial differentialequations is presented. Since, in this new scheme, the particles are followedbackward in time, it provides great flexibility in choosing critical points inphase-space at which to concentrate the launching of particles and therebyminimizing the statistical noise of the sought solution. The trajectory of aparticle, Xi(t), is given by the numerical solution to the stochasticdifferential equation naturally associated with the parabolic equation. Theweight of a particle is given by the initial condition of the parabolicequation at the point Xi(0). Another unique advantage of this new Monte-Carlomethod is that it produces a smooth solution, i.e. without delta-functions, bysumming up the weights according to the Feynman-Kac formula.
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