  In this paper we investigate the mean square asymptotic stability of a
perturbed scalar linear stochastic functional differential equation.
Specifically, we are able to give necessary and sufficient conditions on the
forcing terms for convergence of the mean square, exponential convergence of
the mean square, and integrability of the mean square of solutions. It is also
essential that the underlying unperturbed SFDE is mean square asymptotically
stable for these results to hold.
