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We give a unified method to derive the strong convergence rate of thebackward 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 withpolynomial growth coefficients. We also generalize the argument to theGalerkin-based backward Euler scheme of SPDEs with polynomial growthcoefficients driven by multiplicative trace-class noise.

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