  To our knowledge, the existing measure approximation theory requires the
diffusion term of the stochastic delay differential equations (SDDEs) to be
globally Lipschitz continuous. Our work is to develop a new explicit numerical
method for SDDEs with the nonlinear diffusion term and establish the measure
approximation theory. Precisely, we construct a function-valued explicit
truncated Euler-Maruyama segment process (TEMSP) and prove that it admits a
unique ergodic numerical invariant measure. We also prove that the numerical
invariant measure converges to the underlying one of SDDE in the Fortet-Mourier
distance. Finally, we give an example and numerical simulations to support our
theory.
