We construct a family of explicit tamed Euler--Maruyama (TEM) schemes, which can preserve the same Lyapunov structure 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.

翻译：我们构建了一类显式驯化Euler--Maruyama（TEM）格式，该格式能够保持由乘性噪声驱动的超线性随机常微分方程（SODE）的相同Lyapunov结构。这些TEM格式被证明继承了所考虑SODE的几何遍历性，并以最优强收敛阶收敛。数值实验验证了我们的理论结果。