Stability and Boundedness of Stochastic Integro-Delay Differential Equations

Abstract

This work addresses stochastic integro-delay differential equations (SIDDEs) of second order with two constant delays. In the study, two new results including sufficient conditions on stochastic asymptotic stability and stochastic boundedness in probability of solutions of the given SIDDEs are proved. The proofs of new results are done by using a Lyapunov-Krasovskii functional (L-KF) as a basic tool. To demonstrate the validity of the obtained results, two examples are provided. According to a comparison with previous literature, the results of this study are new and also allow new contributions to the qualitative theory of SIDDEs.