Geometric Ergodicity and Strong Error Estimates for Tamed Schemes of Super-linear SODEs
arXiv:2411.060491.76 citationsh-index: 3
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Provides rigorous numerical methods for long-time simulation of super-linear SODEs, addressing a known bottleneck in stochastic computation.
The paper constructs explicit tamed Euler-Maruyama schemes for super-linear SODEs with multiplicative noise, proving they preserve geometric ergodicity and achieve optimal strong convergence orders.
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.