Stability in linear scalar neutral stochastic integro-differential equations with variable delays

H. Messaoudi, A. Ardjouni, S. Zitouni

In this study, for a linear scalar neutral stochastic integro-differential equation with variable delays, we apply the contraction mapping theorem and provide some novel criteria to guarantee that the zero solution is asymptotically mean square stable. Also demonstrated is an asymptotic mean square stability theorem with a sufficient and necessary condition. Finally, we provide an example to further clarify our findings.I 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 18(2) (2025), pp. 53-66