Summary: The paper discusses both
th moment and almost sure exponential stability of solutions to neutral stochastic functional differential equations and neutral stochastic differential delay equations, by using the Razumikhin-type technique. The main goal is to find sufficient stability conditions that could be verified more easily then by using the usual method with Lyapunov functionals. The analysis is based on a paper of X. Mao
[SIAM J. Math. Anal. 28, No. 2, 389–401 (1997; Zbl 0876.60047
)], referring to mean square and almost sure exponential stability.