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<p>It is difficult to obtain explicit analytical expressions for the solutions of SDEs. Consequently, research on numerical methods for SDEs has been extensive across various application domains. In this article, we introduce a new explicit tamed Euler-Maruyama method for stochastic differential equations characterized by superlinearly growing drift coefficients. The convergence and exponential mean-square stability of the proposed scheme have been investigated, and several numerical simulation results have been presented to substantiate the theoretical findings. Examples show that the new tamed approach achieves a convergence rate 0.5 and works well even with large time step sizes. Examples also confirm the stability of numerical solutions.</p>

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A note on an explicit numerical scheme for SDEs with superlinear coefficients

  • 期刊论文

  • 发表日期：

    2025年6月17日

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  • Mingtian Tang,
  • Zaiming Liu,
  • Yunyan Wang

摘要

It is difficult to obtain explicit analytical expressions for the solutions of SDEs. Consequently, research on numerical methods for SDEs has been extensive across various application domains. In this article, we introduce a new explicit tamed Euler-Maruyama method for stochastic differential equations characterized by superlinearly growing drift coefficients. The convergence and exponential mean-square stability of the proposed scheme have been investigated, and several numerical simulation results have been presented to substantiate the theoretical findings. Examples show that the new tamed approach achieves a convergence rate 0.5 and works well even with large time step sizes. Examples also confirm the stability of numerical solutions.