Malliavin Calculus for Degenerate Stochastic Functional Differential Equations

Consider the solution {X(t); t∈[?r,T]} of the following stochastic functional differential equation: $$dX(t)=biggl{int_{-r}^{0}rho(s)X(t+s),ds+A_{0}(t,X(t))biggr}dt+sum_{i=1}^{m}A_{i}(t,X(t)),dW^{i}(t),$$ where ρ(t) is an ?-valued function on [?r,0], and {W(t); t∈[0,T]} is an m-dimensional Brownian motion. The main purpose is to study the smoothness of the probability density of X(T) with respect to the Lebesgue measure.