High-order strong methods for stochastic differential equations with colored noises

Abstract

The key difficulty to develop efficient high-order methods for integrating stochastic differential equations lies in the calculations of the multiple stochastic integrals. This letter suggests a scheme to compute the stochastic integrals for the colored noises based on the white noise representation. The multiple stochastic integrals involving one and two stationary noises can be conveniently generated together with noises using the discrete Fourier transformation. Based on the calculated stochastic integrals, we obtain simple fourth-order and third-order strong methods for equations with a single and multiple noises, respectively. Numerical tests verify the accuracy of the suggested methods.