Stability of Numerical Solution to Pantograph Stochastic Functional Differential Equations

TL;DR

This paper investigates the convergence and stability properties of Euler-Maruyama numerical solutions for pantograph stochastic functional differential equations, demonstrating almost sure polynomial and exponential stability.

Contribution

It provides new theoretical results on the stability of numerical solutions for pantograph stochastic differential equations, extending existing convergence analysis.

Findings

Numerical solutions converge under specified conditions.

Solutions exhibit almost sure polynomial stability.

Solutions demonstrate exponential stability.

Abstract

In this paper, we study the convergence of the Euler-Maruyama numerical solutions for pantograph stochastic functional differential equations which was proposed in [11]. We also show that the numerical solutions have the properties of almost surely polynomial stability and exponential stability with the help of semi-martingale convergence theorem.