A Note on Exponential Stability for Numerical Solution of Neutral Stochastic Functional Differential Equations

Abstract

This paper examines the numerical solutions of the neutral stochastic functional differential equation. This study establishes the discrete stochastic Razumikhin-type theorem to investigate the exponential stability in the mean square sense of the Euler–Maruyama numerical solution to this equation. In addition, the Borel–Cantelli lemma and the stochastic analysis theory are incorporated to discuss the almost sure exponential stability for this numerical solution of such equations.

Keywords

• neutral stochastic functional differential equations
• Euler–Maruyama method
• discrete Razumikhin-type theorem
• exponential stability
• numerical solution