$L^p$-Convergence Rate of Backward Euler Schemes for Monotone SDEs

Abstract

We give a unified method to derive the strong convergence rate of the backward Euler scheme for monotone SDEs in $L^p(\Omega )$-norm, with general $p\ge 4$. The results are applied to the backward Euler scheme of SODEs with polynomial growth coefficients. We also generalize the argument to the Galerkin-based backward Euler scheme of SPDEs with polynomial growth coefficients driven by multiplicative trace-class noise.

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Cited by in corpus (4)

• Numerical Unique Ergodicity of Monotone SDEs driven by Nondegenerate Multiplicative Noise
• Central limit theorem for temporal average of backward Euler--Maruyama method
• Numerical Ergodicity and Uniform Estimate of Monotone SPDEs Driven by Multiplicative Noise
• Harnack Inequalities and Ergodicity of Stochastic Reaction-Diffusion Equation in $L^p$