Stability of Numerical Solution to Pantograph Stochastic Functional Differential Equations (2108.01248v1)

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.