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

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.

Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays

“…The existence and uniqueness results for abstract stochastic delay differential equation driven by fractional Brownian motions have been studied in [7]. In particular the stability investigation of stochastic differential equations has been investigated by several authors [8][9][10][11][12][13][14][15].…”