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Geometric Ergodicity and Optimal Error Estimates for a Class of Novel Tamed Schemes to Super-linear Stochastic PDEs
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We construct a class of novel tamed schemes that can preserve the original Lyapunov functional for super-linear stochastic PDEs (SPDEs), including the stochastic Allen--Cahn equation, driven by multiplicative or additive noise, and provide a rigorous analysis of their long-time unconditional stability. We also show that the corresponding Galerkin-based fully discrete tamed schemes inherit the geometric ergodicity of the SPDEs and establish their convergence towards the SPDEs with optimal strong rates in both the multiplicative and additive noise cases.
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Cited by 2 Pith papers
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Uniform-in-Time Weak and Ergodic Error Estimates of a Nonlinearity-Explicit Full Discretization for Superlinear SPDEs Driven by Multiplicative Noise
A tamed Euler-Galerkin scheme for superlinear SPDEs with multiplicative noise converges with essentially first-order temporal and 1+γ/2 spatial weak error uniformly in time, yielding an ergodic invariant-measure error bound.
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A modified tamed scheme for stochastic differential equations with superlinear drifts
A cutoff-based taming of the drift lets explicit Euler-type schemes keep their usual strong and weak convergence orders for SDEs with superlinear drift, with a near-sharp uniform-in-time KL bound for tamed SGLD.
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