Mean square exponential and non-exponential asymptotic stability of impulsive stochastic Volterra equations

* Correspondence: [email protected] Department of mathematics, Shanghai Jiaotong University, Shanghai, 200240, China Full list of author information is available at the end of the article Abstract In this article, some inequalities on convolution equations are presented firstly. The mean square stability of the zero solution of the impulsive stochastic Volterra equation is studied by using obtained inequalities on Liapunov function, including mean square exponential and non-exponential asymptotic stability. Several sufficient conditions for the mean square stability are presented. Results in this article indicate that not only the impulse intensity but also the time of impulse can influence the stability of the systems. At last, an example is given to show application of some obtained results. Mathematics classification Primary(2000): 60H10, 60F15, 60J70, 34F05.