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Demonstrates optimal error rates in tamed schemes for super-linear SODEs, suggesting effective noise handling.
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.
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Liu et al. (2026) studied this question.
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