PATH INTEGRAL SOLUTION OF THE FOKKER-PLANCK EQUATION VIA A GENERALIZED TROTTER FORMULA

Two novel classes of the short time propagators for the multi-dimensional Fokker-Planck equation (FPE) are developed by using a generalized Trotter formula. These are definable up to an arbitrary function of a time increment. Their efficiency is very sensitive to the choice of this function several forms of which are proposed. The short time propagators thus derived allow for much more rapid convergence of path integral computer simulations than the standard one. In some cases they can be used as the global approximations for the single step propagator valid in the entire time domain.