SummaryThis paper is concerned with the exponential ultimate boundedness problems for the impulsive stochastic delay difference systems. Several sufficient conditions on the globalpth moment exponential ultimate boundedness are presented by using the Lyapunov methods and the algebraic inequality techniques, and the estimated exponential convergence rate and the ultimate bound are provided as well. As an application, the boundedness criteria are applied to a class of discrete impulsive stochastic neural networks with delays. The obtained results show that the impulses not only can stabilize an unstable stochastic difference delay system but also can make an unbounded stochastic difference delay system into a bounded system. Examples and simulations are also provided to demonstrate the effectiveness of the derived theoretical results.