Lyapunov functionals and practical stability for stochastic differential delay equations with general decay rate

Abstract

This paper stands for the almost sure practical stability of nonlinear stochastic differential delay equations (SDDEs) with a general decay rate. We establish some sufficient conditions based upon the construction of appropriate Lyapunov functionals. Furthermore, we provide some numerical examples to validate the effectiveness of the abstract results of this paper.

Keywords

• stochastic delay systems
• almost sure practical stability
• decay function
• lyapunov functional
• itô formula