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| 摘要: |
| Tang和Mao在[1]中建立了对数截断Euler-Maruyama方法,该方法是一种具有竞争力的保正性显式数值算法。
然而,其理论假设是限制性的,仅适用于标量随机微分方程(SDE)，限制了多维情形的应用。本文旨在通过修正原假设条件,将这一方法推广至多维SDE,并建立其强收敛性结果。具体而言,若SDE对足够大的
p 阶矩存在有限性,则多维SDE的对数截断Euler-Maruyama方法将保持与标量情形一致的强收敛阶率(1/2阶)。 |
| 关键词: 多维随机微分方程 保正性 对数截断EM方法 数值模拟 |
| DOI： |
| 分类号:O241 |
| 基金项目: |
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| Logarithmic truncated EM Method for a Class of Multi-dimensional Stochastic Differential Equations |
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Huang Yongjie,赵君一郎
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| Abstract: |
| Tang and Mao in [1] established the logarithmic truncation Euler-Maruyama method for scalar SDEs, which is a competitive positivity preserving explicit numerical method.
However, assumptions for the logarithmic truncated Euler-Maruyama method used in their work are restrictive which exclude multi-dimensional SDEs.
The main purpose of this paper is to modify the assumptions, extend the logarithmic truncated EM method to multi-dimensional SDEs and establish a strong convergence result. Specifically, if the SDE admits finite
p-th moments for sufficiently large $p$, the logarithmic truncated EM method for multi-dimensional SDEs retains the same strong convergence rate of order
1/2 as in the scalar case. |
| Key words: Multi-dimensional Stochastic differential equations Positivity preserving The logarithmic truncated EM Method Numerical simulation |
