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The improvement of the truncated Euler-Maruyama method for non-Lipschitz stochastic differential equations

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Abstract

This paper is concerned with the numerical approximations for stochastic differential equations with non-Lipschitz drift or diffusion coefficients. A modified truncated Euler-Maruyama discretization scheme is developed. Moreover, by establishing the criteria on stochastic C-stability and B-consistency of the truncated Euler-Maruyama method, we obtain the strong convergence and the convergence rate of the numerical method. Finally, numerical examples are given to illustrate our theoretical results.

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Acknowledgements

The authors would like to thank the editors and referees for their very helpful comments and suggestions. The authors would like to thank the financial support by the Anhui University Natural Science Research Project(KJ2021A0107) and the Shanghai Sailing Program (21YF1416100).

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Authors and Affiliations

  1. Department of Mathematics, Anhui Normal University, Wuhu, 241000, China

    Weijun Zhan

  2. School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China

    Yuyuan Li

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  1. Weijun Zhan
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Correspondence to Yuyuan Li.

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Zhan, W., Li, Y. The improvement of the truncated Euler-Maruyama method for non-Lipschitz stochastic differential equations. Adv Comput Math 50, 30 (2024). https://doi.org/10.1007/s10444-024-10131-w

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  • DOI: https://doi.org/10.1007/s10444-024-10131-w

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