Operator expansions in stochastic dynamics

Higher-order operator factorizations are a powerful tool for efficiently treating classical mechanics. This paper presents an application of the method to stochastic dynamics. Using a fourth-order symmetric decomposition of the time evolution operator, we arrive at a high-accuracy scheme for propagating the distribution function in time. Its power is demonstrated by means of two problems, namely, the dynamics of a colored noise process and a Brownian particle in a potential field. The applications show our method to be superior over the standard propagation scheme based on the Trotter splitting in that it allows much larger time steps with no loss of precision. [S1063-651X(98)00902-7].