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<p>In recent years, the strong convergence analysis of positivity-preserving numerical methods and the weak convergence analysis of numerical methods for stochastic differential equations in general have garnered widespread attention. However, research focusing on the weak convergence analysis of positivity-preserving methods remains limited. In particular, the weak convergence analysis of these methods in the multi-dimensional setting remains unexplored, which constitutes the core objective of the present work. In this paper, we first prove the existence and uniqueness of positive strong solution of the underlying equations under certain conditions. Then, we investigate the weak convergence of the positivity-preserving truncated Euler–Maruyama method and demonstrate that, under additional conditions, its convergence order can be made arbitrarily close to 1. Lastly, numerical experiments are conducted to validate the theoretical findings.</p>

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Weak convergence rate of positivity-preserving truncated Euler–Maruyama method for multi-dimensional stochastic differential equations with positive solutions

  • 期刊论文

  • 发表日期：

    2026年3月13日

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  • Xingwei Hu,
  • Xinjie Dai,
  • Aiguo Xiao

摘要

In recent years, the strong convergence analysis of positivity-preserving numerical methods and the weak convergence analysis of numerical methods for stochastic differential equations in general have garnered widespread attention. However, research focusing on the weak convergence analysis of positivity-preserving methods remains limited. In particular, the weak convergence analysis of these methods in the multi-dimensional setting remains unexplored, which constitutes the core objective of the present work. In this paper, we first prove the existence and uniqueness of positive strong solution of the underlying equations under certain conditions. Then, we investigate the weak convergence of the positivity-preserving truncated Euler–Maruyama method and demonstrate that, under additional conditions, its convergence order can be made arbitrarily close to 1. Lastly, numerical experiments are conducted to validate the theoretical findings.