河南科技大学学报（自然科学版）2025，Vol.46Issue(2)：95-104,10.DOI:10.15926/j.cnki.issn1672-6871.2025.02.011
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
摘要
Abstract
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Key words
stochastic pantograph differential equations/Lévy noise/non-Lipschitz conditions/Euler method/numerical solution分类
数学引用本文复制引用
梁飞,张丽洁..非Lipschitz条件下Lévy噪声扰动的随机比例型微分方程的数值解[J].河南科技大学学报（自然科学版）,2025,46(2):95-104,10.基金项目
国家自然科学基金项目(42271309) （42271309）
