  In this paper, a general theorem on the equivalence of pth moment stability
between stochastic differential delay equations (SDDEs) and their numerical
methods is proved under the assumptions that the numerical methods are strongly
convergent and have the bouneded $p$th moment in the finite time. The truncated
Euler-Maruyama (EM) method is studied as an example to illustrate that the
theorem indeed covers a large ranges of SDDEs. Alongside the investigation of
the truncated EM method, the requirements on the step size of the method are
significantly released compared with the work, where the method was initially
proposed.
