| 摘要: |
| 本文研究了一类多维随机微分方程(SDEs)的保正性数值求解问题.利用修正原有理论中的假设条件并结合对数变换的性质,构造新型截断函数的方法.获得了该数值方法的强收敛性结果,证明了在一定条件下数值解的Lp收敛性,且强收敛速率可达1/2阶.推广了原有方法的结果,成功将对数截断EM方法的应用范围从标量SDEs拓展至多维SDEs. |
| 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:O211.63 |
| 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 Yong-jie, ZHAO Jun-yilang
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School of Mathematics, Southwest Jiaotong University, Sichuan 611756, China
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| Abstract: |
| This paper studies the problem of preserving positivity in the numerical solution of a class of multi-dimensional stochastic differential equations (SDEs). By modifying the assumptions in the original theory and combining the properties of logarithmic transformation, a new method for constructing truncation functions is developed. The strong convergence result of this numerical method is obtained, and it is proved that the Lp convergence of the numerical solution holds under certain conditions, with the strong convergence rate reaching the 1=2 order. The results of the original method are generalized, successfully expanding the application scope of the logarithmic truncation EM method from scalar SDEs to multi-dimensional SDEs. |
| Key words: multi-dimensional stochastic differential equations positivity preserving the logarithmic truncated EM method numerical simulation |
