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\(L^p\)-convergence rate of backward Euler schemes for monotone SDEs

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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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Acknowledgements

We thank the anonymous referees for very helpful remarks and suggestions. The author is supported by National Natural Science Foundation of China, No. 12101296 and SUSTech fund, No. Y01286232.

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  1. Department of Mathematics, Southern University of Science and Technology, 1088 Xueyuan Avenue, Shenzhen, 518055, People’s Republic of China

    Zhihui Liu

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  1. Zhihui Liu
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Correspondence to Zhihui Liu.

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Communicated by Axel Målqvist.

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Liu, Z. \(L^p\)-convergence rate of backward Euler schemes for monotone SDEs. Bit Numer Math 62, 1573–1590 (2022). https://doi.org/10.1007/s10543-022-00923-1

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