The widely used Heun algorithm for the numerical integration of stochastic differential equations (SDEs) is critically re-examined. We discuss and evaluate several alternative implementations, motivated by the fact that the standard Heun scheme is constructed from a low-order integrator. The convergence, stability, and equilibrium properties of these alternatives are assessed through extensive numerical simulations. Our results confirm that the standard Heun scheme remains a benchmark integration algorithm for SDEs due to its robust performance. As a byproduct of this analysis, we also disprove a previous claim in the literature regarding the strong convergence of the Heun scheme.

翻译：本文对广泛应用于随机微分方程数值积分的Heun算法进行了批判性重审。鉴于标准Heun格式源自低阶积分器的事实，我们讨论并评估了若干替代实施方案。通过大量数值模拟，对这些替代方案的收敛性、稳定性及平衡特性进行了系统评估。研究结果证实，标准Heun格式凭借其稳健性能，仍是随机微分方程数值积分的基准算法。作为本研究的副产品，我们同时证伪了文献中关于Heun格式强收敛性的既有论断。