Weak convergence of delay sdes with applications to caratheodory approximation

In this paper, we consider a fundamental class of stochastic differ-ential equations with time delays. Our aim is to investigate the weak conver-gence with respect to delay parameter of the solutions. Based on the techniques of Malliavin calculus, we obtain an explicit estimate for the rate of convergence. An application to the Caratheodory approximation scheme of stochastic dif-ferential equations is provided as well.