Asymptotic behavior of mild solutions to stochastic neutral functional differential equations with delay

This paper aims to discuss the existence, uniqueness and continuous dependence of mild solution of a class of non-autonomous stochastic neutral functional differential equations with state-dependent delay. Firstly, by using operator theory and estimates of the nonlinear term, we obtain the existence, uniqueness and continuous dependence of our concern system. Secondly, through the Arzelà–Ascoli theorem, the Schauder fixed point theorem and operator theory, we discuss the global existence asymptotic behavior of mild solution of our concern system. Then, the existence of a global forward attracting set in the mean square topology is discussed. Finally, we give an example to verify the validity of the obtained results.