Exponential ultimate boundedness of impulsive stochastic delay differential equations

This paper is devoted to the investigation of the ultimate boundedness of impulsive stochastic delay differential equations. The pth moment global exponential ultimate boundedness criteria are obtained based on the Ito formula and the successful construction of suitable Lyapunov functionals, and the estimated exponential convergence rate and the ultimate bound are provided as well. It is shown that unbounded stochastic delay differential equations can be turned into bounded ones by impulses. (C) 2018 Elsevier Ltd. All rights reserved.