Asymptotic behaviour and boundedness of solutions for third-order stochastic differential equation with multi-delay

Abstract

Abstract In the present paper, we study stochastic stability and stochastic boundedness for the stochastic differential equation (SDE) with multi-delay of third order. The derived results extend and improve some earlier results in the relevant literature, which are related to the qualitative properties of solutions to third-order delay differential equations (DDEs) and SDEs with multi-delay. Two examples are given to illustrate the results.

Keywords

• Delay differential equations (DDEs)
• Stochastic delay differential equations (SDDEs)
• Multi-delay
• Stochastic stability
• Stochastic boundedness