Split-step Milstein methods for multi-channel stiff stochastic differential systems

TL;DR

This paper analyzes split-step Milstein methods for solving stiff multi-channel stochastic differential equations, demonstrating their convergence and stability properties through theoretical analysis and numerical experiments.

Contribution

It introduces and evaluates split-step Milstein methods specifically tailored for multi-channel noise in stiff stochastic systems, including stability analysis and practical performance.

Findings

Methods achieve strong convergence order

Stability matrices are explicitly characterized

Numerical examples confirm effectiveness

Abstract

We consider split-step Milstein methods for the solution of stiff stochastic differential equations with an emphasis on systems driven by multi-channel noise. We show their strong order of convergence and investigate mean-square stability properties for different noise and drift structures. The stability matrices are established in a form convenient for analyzing their impact arising from different deterministic drift integrators. Numerical examples are provided to illustrate the effectiveness and reliability of these methods.