Improved stability conditions for a class of stochastic Volterra–Levin equations

摘要

In this paper, we study the mean square asymptotic stability of a class of generalized nonlinear stochastic Volterra–Levin equations by using fixed point theory. Several sufficient conditions are established for ensuring that the equation is mean square asymptotically stable as well as exponentially stable. The main results are new which generalize and improve some well-known results in Burton (2006) [4] and Luo (2010) [18]. Finally, two examples are given to illustrate our results.