Numerical Solutions for Stochastic Pantograph Differential Equations with Lévy Noise under Non-Lipschitz Conditions
LIANG Fei
ZHANG Lijie
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.
Keywords：stochastic pantograph differential equationsLévy noisenon-Lipschitz conditionsEuler methodnumerical solution
Publication Date：2025-04-25
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：10( 95-104 )