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<p>We construct a family of explicit tamed Euler–Maruyama (TEM) schemes, which can preserve the same Lyapunov function for super-linear stochastic ordinary differential equations (SODEs) driven by multiplicative noise. These TEM schemes are shown to inherit the geometric ergodicity of the considered SODEs and converge with optimal strong convergence orders. Numerical experiments verify our theoretical results.</p>

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Geometric Ergodicity and Strong Error Estimates for Tamed Schemes of Super-linear SODEs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月27日

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  • Zhihui Liu,
  • Xiaoming Wu

摘要

We construct a family of explicit tamed Euler–Maruyama (TEM) schemes, which can preserve the same Lyapunov function for super-linear stochastic ordinary differential equations (SODEs) driven by multiplicative noise. These TEM schemes are shown to inherit the geometric ergodicity of the considered SODEs and converge with optimal strong convergence orders. Numerical experiments verify our theoretical results.