Modify the Improved Euler scheme to integrate stochastic differential equations

Abstract

A practical and new Runge--Kutta numerical scheme for stochastic differential equations is explored. Numerical examples demonstrate the strong convergence of the method. The first order strong convergence is then proved using Ito integrals for both Ito and Stratonovich interpretations. As a straightforward modification of the deterministic Improved Euler/Heun method, the method is a good entry level scheme for stochastic differential equations, especially in conjunction with Higham's introduction [SIAM Review, 43:525--546, 2001].

References in corpus (1)

• Normal form transforms separate slow and fast modes in stochastic dynamical systems

Cited by in corpus (8)

• Committor Functions for Climate Phenomena at the Predictability Margin: The example of El Niño Southern Oscillation in the Jin and Timmerman model
• Gotta Go Fast When Generating Data with Score-Based Models
• Memory-induced oscillations of a driven particle in a dissipative correlated medium
• DriftRec: Adapting diffusion models to blind JPEG restoration
• Controlled pattern formation of stochastic Cucker-Smale systems with network structures
• Almost Surely Stable Deep Dynamics
• Numerical integration of ordinary differential equations with rapidly oscillatory factors
• Testing Inflationary Cosmology