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<p>This paper is concerned with long-time strong approximations of SDEs with non-globally Lipschitz coefficients. Under certain non-globally Lipschitz conditions, a long-time version of fundamental strong convergence theorem is established for general one-step time discretization schemes. With the aid of the fundamental strong convergence theorem, we prove the expected strong convergence rate over infinite time for two types of schemes such as the backward Euler method and the projected Euler method in non-globally Lipschitz settings. Numerical examples are finally reported to confirm our findings.</p>

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Strong convergence rates for long-time approximations of SDEs with non-globally Lipschitz continuous coefficients

  • 期刊论文

  • 发表日期：

    2025年11月4日

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  • Xiaoming Wu,
  • Xiaojie Wang

摘要

This paper is concerned with long-time strong approximations of SDEs with non-globally Lipschitz coefficients. Under certain non-globally Lipschitz conditions, a long-time version of fundamental strong convergence theorem is established for general one-step time discretization schemes. With the aid of the fundamental strong convergence theorem, we prove the expected strong convergence rate over infinite time for two types of schemes such as the backward Euler method and the projected Euler method in non-globally Lipschitz settings. Numerical examples are finally reported to confirm our findings.