Exponential stability in mean square of impulsive stochastic difference equations with continuous time

So far there have been few results presented on the exponential stability in mean square for impulsive stochastic difference equations with continuous time. The main aim of this work is to close this gap. Unlike earlier studies, ours does not make use of general methods such as Lyapunov methods, Itô formula methods and so forth. However, we obtain the desired result by establishing a difference inequality with continuous time. Moreover, the result obtained can be applied to stochastic difference equations, without impulsive effects, with continuous time. Finally, we construct an example to illustrate the effectiveness of our result.