非Lipschitz条件下Lévy噪声扰动的随机比例型微分方程的数值解  

Numerical Solutions for Stochastic Pantograph Differential Equations with Lévy Noise under Non-Lipschitz Conditions

作　　者：梁飞[1] 张丽洁 LIANG Fei;ZHANG Lijie(College of Science,Xi’an University of Science and Technology,Xi’an 710699,China)

机构地区：[1]西安科技大学理学院,陕西西安710699

出　　处：《河南科技大学学报(自然科学版)》2025年第2期95-104,M0008,共11页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(42271309)。

摘　　要：针对满足非Lipschitz条件的Lévy噪声扰动的随机比例型微分方程,首先证明了方程的精确解在非Lipschitz条件下以大概率存在于紧集中;其次运用Euler方法构造出方程的数值解,并证明了数值解在均方意义下依概率收敛于精确解;最后通过一个例子验证了结论的有效性。This paper investigates stochastic pantograph differential equations driven by Lévy noise under non-Lipschitz conditions.Initially,it is established that the exact solution of the equation exists with high probability within a compact set,even under the constraints of non-Lipschitz conditions.Subsequently,the Euler method is utilized to develop a numerical solution,and it is rigorously shown that the numerical solution converges to the exact solution in probability within the mean square framework.Finally,a concrete example is presented to substantiate the validity and efficacy of the theoretical findings.

关 键 词：随机比例型微分方程 Lévy噪声 非LIPSCHITZ条件 EULER方法 数值解 

分 类 号：O241.8[理学—计算数学]