Alternative Simulating Technique for Periodic Motion in the Presence of Multiplicative White Noise

An effective approach for simulating the periodic motion of an overdamped particle subjected to a multiplicative white-noise source is described. The accurate calculations for the velocity of the particle and its correlation function can be realized by introducing an inertial term. The results show that fluctuation around a time-averaged quantity increases with decreasing time step in the overdamped white-noise algorithm, however, a massive white-noise technique greatly reduces this spurious drift. In particular, the present algorithm converges on the correct values of the calculated quantities, while the mass of the particle approaches to zero.