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

TL;DR

This paper introduces high-order strong numerical methods for stochastic differential equations with colored noises, utilizing white noise representation and Fourier transforms to efficiently compute stochastic integrals, resulting in accurate fourth- and third-order schemes.

Contribution

The paper develops novel high-order strong methods for SDEs with colored noises using a white noise representation and Fourier transform techniques, enabling efficient stochastic integral computation.

Findings

Methods achieve fourth- and third-order accuracy.

Numerical tests confirm the methods' effectiveness.

Efficient computation of stochastic integrals for 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.